What is the biblical basis for only keeping the weekly Sabbath while disregarding all the other feasts/holy convocations (Lev 23, Num 28, 29)?

The Days in the Seventh Month
Since Jesus' death on the cross is the once for all sacrifice for sins, no Christian should observe the Day of Atonement which occurs in the seventh month of the year. Jesus' death on cross took place during the time of Passover which comes in the first month of the year. This suggests Christians should compare the two months to more completely understand the timing of Jesus' sacrifice:

Seventh Month                         First Month
1  Trumpets                           1  First day of the year
10 Day of Atonement                   10 Choose the Passover Lamb
14 [Build booth]                      14 Passover - kill the Lamb
15 Day of rest - Tabernacles begins   15 Day of rest - Unleavened Bread begins
21 Tabernacles ends                   21 Day of rest - Unleavened Bread ends
22 Day of rest after Tabernacles

The Day of Atonement is only a type or shadow of the real sacrifice which was to come. Today it is a reminder of the inefficacy of the sacrificial system to correct the problem of sin which could only be done by the Lamb of God who takes away the sin of the world. Historically, the Day of Atonement remembrance which comes in the seventh month of the year simply shows the significance of the number seven while pointing to the actual time in the future on which the Passover Lamb would be revealed before being offered. This day most likely corresponds to Jesus' Triumphal Entry into Jerusalem and cleansing of the Temple.

The Feast of Tabernacles follows the Day of Atonement. Since the first day is a day of no work, the booth in which one is to spend the next 7-days must be completed on the 14^th day of the month. This corresponds to the day the Passover Lamb is to be killed. Thus, Tabernacles points the Christian to the seven days of Unleavened Bread. While this parallel could be used to argue Unleavened Bread should be observed, comparing both feasts shows that neither is adequate to fully remember the sacrifice of the cross which brings both the Living Bread and a "tabernacle" for those who believe. In other words, the 7-days of Unleavened Bread now serve only as a reminder of the unfinished work of the original Passover of bringing the people out of Egypt. Today it is a reminder of the sacrifice of the cross which brings people out of bondage to sin and into Jesus' Father's House. The Christian has both Living Bread and a Tabernacle: a combination not found in any single annual observation.

Other than "Trumpets" all of the Feast days in the seventh month can be seen as "types" or shadows pointing to the sacrifice of Jesus which would occur in the first month of the year. However, after the seven days of Tabernacles, the people were to observe one final day:

...On the eighth day you shall hold a holy convocation and present a food offering to the LORD. It is a solemn assembly; you shall not do any ordinary work. (Leviticus 23:36)

This eighth day observance concludes the annual calendar and it summarizes the completed work of Jesus. That is, this day rightly summarizes the annual calendar in the light of Jesus' death and resurrection. This "day" has no name and is like the weekly Sabbath except it requires no animal sacrifice. Arguably, it is the one annual day which comes closest to remembering the completed work of the cross, if one remained in the booth for the extra day and shared in the food offering to the LORD.

"The" Sabbath Rest
The primary reason for the "remembering" any day is to remember God's work:

• The weekly Sabbath: God's work of creation and blessing the seventh day
• The annual days: God's bringing the people out of bondage to Pharaoh and slavery in Egypt

Not only is the work of creation a "greater" work; it was God's first work and, arguably, a work which should be recognized and acknowledged by all mankind, not just those who accept His work of redemption.

From this historical perspective the Bible states the rest which the Sabbath remembers was the first day experienced by man and will be a day in the future which the people of God will experience:

⁸ For if Joshua had given them rest, God would not have spoken of another day later on. ⁹ So then, there remains a Sabbath rest for the people of God, ¹⁰ for whoever has entered God's rest has also rested from his works as God did from his. (Hebrews 4) [ESV]

It is clear from both the Old Testament and New the rest envisioned in the letter to the Hebrews was not experienced by those who received the explicit instructions after being brought out of Egypt¹or by those to whom the letter is addressed. In other words, just as there was an initial day of rest which the first man and woman experienced, there will be a future day of rest, literally "Sabbath-rest" σαββατισμός, not Sabbath σάββατον rest κατάπαυσις which the people of God will experience. In this way observing the Sabbath now remembers both mankind's first rest living with God and that rest with Him in the future:

¹ Then I saw a new heaven and a new earth, for the first heaven and the first earth had passed away, and the sea was no more. ² And I saw the holy city, new Jerusalem, coming down out of heaven from God, prepared as a bride adorned for her husband. ³ And I heard a loud voice from the throne saying, “Behold, the dwelling place of God is with man. He will dwell with them, and they will be his people, and God himself will be with them as their God. ⁴ He will wipe away every tear from their eyes, and death shall be no more, neither shall there be mourning, nor crying, nor pain anymore, for the former things have passed away.” (Revelation 21)

After God rested on the seventh day, He continued to work (John 5:17). Once His final works of re-creation and redemption are completed, mankind will experience the promised Sabbath-rest. The "eighth day" of Tabernacles points to this future day.

The Other Annual Days
The first days which are instructed to be remembered are Passover and Unleavened Bread:

¹ The LORD said to Moses and Aaron in the land of Egypt, ² “This month shall be for you the beginning of months. It shall be the first month of the year for you. ³ Tell all the congregation of Israel that on the tenth day of this month every man shall take a lamb according to their fathers' houses, a lamb for a household. ⁴ And if the household is too small for a lamb, then he and his nearest neighbor shall take according to the number of persons; according to what each can eat you shall make your count for the lamb. ⁵ Your lamb shall be without blemish, a male a year old. You may take it from the sheep or from the goats, ⁶ and you shall keep it until the fourteenth day of this month, when the whole assembly of the congregation of Israel shall kill their lambs at twilight.

¹⁴ “This day shall be for you a memorial day, and you shall keep it as a feast to the LORD; throughout your generations, as a statute forever, you shall keep it as a feast. ¹⁵ Seven days you shall eat unleavened bread. On the first day you shall remove leaven out of your houses, for if anyone eats what is leavened, from the first day until the seventh day, that person shall be cut off from Israel. ¹⁶ On the first day you shall hold a holy assembly, and on the seventh day a holy assembly. No work shall be done on those days. But what everyone needs to eat, that alone may be prepared by you. ¹⁷ And you shall observe the Feast of Unleavened Bread, for on this very day I brought your hosts out of the land of Egypt. Therefore you shall observe this day, throughout your generations, as a statute forever. ¹⁸ In the first month, from the fourteenth day of the month at evening, you shall eat unleavened bread until the twenty-first day of the month at evening.(Exodus 12)

Absent the creation narrative in Genesis, the seven-day period appears to be arbitrary.² However, once the seven days of God's work of creation is known, four things are obvious about the instructions for Passover and Unleavened Bread:

• Both require 7-days
• Both end with a day of rest
• The 7-day period begins on the 14^th day of the first month of the year which was the first day the first man and woman would have been able to observe their first Sabbath.
• The first day is a day of no work, just as the seventh day for the first man and woman (their first day) was a day of no work.

Therefore, it is apparent both the work and remembrance of being brought out of bondage to Pharaoh and slavery in Egypt was patterned after man's experience and remembrance of God's 7-days of creation. That is to say, a present day remembrance of the Sabbath which remembers the 7-days of creation, illuminates God's work of bringing His people out of Egypt.

There was no specific mention of the Sabbath until the second month of that year (cf. Exodus 16). From the details of the manna, the first Sabbath the people observed was was the 22^nd day of that month. This means the people would have already observed at least two Sabbaths before receiving the Ten Commandments.³ It also allows us to "look backward" and place the Sabbaths on the annual calendar:

First Month                              Second Month 
1  Start of the year                     1  [Sabbath #5] 
3  [Sabbath #1]
                                         8  [Sabbath #6]
10 [Sabbath #2] Choose Lamb
14 Passover - Kill Lamb                  14 [Pesach Sheni]
                                         15 [Sabbath #7]
                                         16 First day of manna
17 [Sabbath #3]
18 [First Fruits]
21 Final day of Unleavened Bread
                                         22 First Sabbath observed
24 [Sabbath #4]
                                         29 Second Sabbath observed

God could have identified the Sabbath in the first month but He waited seven Sabbaths before instructing the people to begin to observe the Sabbath. Therefore, the command to observe the Feast of Weeks by counting seven Sabbaths recalls the seven Sabbaths not observed when the people were brought out of Egypt. In addition, the specific day on which the people crossed the Red Sea is not identified, but a case can be made it was on the 17^th. If so, the Feast of First Fruits commemorates the first day the people were truly freed from Pharaoh.

The Christian "Easter Sunday" is a remembrance of the Feast of First Fruits, one of two days on the annual calendar which is determined primarily by a weekly Sabbath. The other is the Feast of Weeks or Pentecost: the day Church began in Jerusalem immediately following the Crucifixion and Resurrection. Many Christians do observe these days, although the remembrance is not necessarily done according to the Jewish annual calendar.

Conclusion
There is good Biblical reason why many of the annual feast days should not be observed as they fail to fully or correctly remember the work of the cross. For example, the Day of Atonement completely misrepresents the timing and/or understanding of Jesus' atoning work.

On the other hand, the continued observation of the Easter and Pentecost may rightly be considered to be "required" days as they do recall the work of Jesus. First Fruits is the day of Resurrection and Pentecost the day the Holy Spirit came upon the disciples. Many Christians continue to observe these days, although not according to their placement on the Jewish calendar, and not acknowledging their full significance to the Judeo-Christian faith.

What is lacking from most Christian calendars is Trumpets and the eighth day of Tabernacles. It may be presumptuous, but it is reasonable to see these two days as pointing to the final Coming of the Lord and as such the Church should treat them as "types" as are the other days in the seventh month and they are not to be observed.

One awaits the Trump of God and one now observes the weekly Sabbath as a regular reminder of both the seventh day of creation and the final day in seventh month (i.e. the completed) annual calendar. This final day is in a sense anticipated when the weekly Sabbath is observed without the required animal sacrifices yet retaining all other elements.

Notes:

1. The first explicit command to observe the Sabbath is given in Exodus 16, before the giving of the Ten Commandments or the Law. Thus the command to "Remember the Sabbath..." (Exodus 20:8) is explicit to continuing the practice of observing the Sabbath on the specific day of the week. Moreover, it was God who gave a physical sign as to identify the day of the week which was the Sabbath (no manna), so the command is not a general principle of "rest:" it is instruction of rest on a specific day.
2. Although there is no astronomic sign or celestial means by which any seven-day period can be tracked. It is only remembered by first identifying the point at which to begin and then counting the days.
3. So "Remember the Sabbath..." means to continue to observe the Sabbath on the day of the week which you have been.