Do Christians believe that more sinful people suffer more on Earth?

The Bible puts God on a throne of the universe judging all nations. Whether they rise or fall it is under his sovereignty:

You have rebuked the nations; you have made the wicked perish; you have blotted out their name forever and ever. The enemy came to an end in everlasting ruins; their cities you rooted out; the very memory of them has perished. But the LORD sits enthroned forever; he has established his throne for justice, and he judges the world with righteousness; he judges the peoples with uprightness. (Psalms 9:5-8)

God’s omnipotence and sovereignty over the world makes this the only possible relationship that he has to the nations and to individuals:

“ ‘See now that I, even I, am he, and there is no god beside me; I kill and I make alive; I wound and I heal; and there is none that can deliver out of my hand. (Deut 32:39)

One of the regular ways God maintains justice is through civil law. Nationally sins may often not brings fruits of judgment to the third or fourth generation of continued disobedience. (Exodus 20:5) For a normal providential perspective, He has provided governments that punish sin doing and made prisons for them. However, in all cases, his own mysterious purposes of will is what dictates the history of the world and rising and falling of powers. In fact in God’s wisdom he often allows the wicked to 'prosper' and even wicked nations as a whole 'prosper'. Although the injustice of this prosperity might bother the righteous who often suffer the Bible say's we need not fret about it (Psalms 37:1):

For I was envious of the arrogant when I saw the prosperity of the wicked. For they have no pangs until death; their bodies are fat and sleek. They are not in trouble as others are; they are not stricken like the rest of mankind. (Psalms 73-5)

So when we approach this subject of suffering particularly on a national level we are approaching God on his throne and we can’t discern how he dispenses justice and in many cases the justice is not administered until the wicked die, but in any case it is from God.

We live in an age that accuses God of being cruel because the innocent suffer, which is just a wicked notion that hold humanity innocent when eternal damnation is its only true desert. The fact is all suffering is the punishment of Adam’s sin upon all humanity and only in Christ is that punishment transferred to the innocent sin of atonement, i.e. Christ’s soul and body which was presented by himself as our high Priest of a new covenant.

For the believer suffering is no longer a punishment as they are righteous and loved but for the wicked the death of their grace is a mild introduction to eternal burning and torment. The bible presents the suffering of this world easy, light and nothing, compared to those of the afterlife. For believers suffering is all light and easy compared to the glory that will be revealed in us and even a source of joy to our soul as we suffer in this world.

One should distinguish though between public judgments for national sins, or smaller scale but very scandalous public sins, and God’s seeming endless patience for our own private sins. If you look at the New Testament we see know miraculous judgments upon people’s private sins. Even a man sleeping with his own father’s wife in 1 Corinthians did not get sick even though it approached scandal. On the other hand when Ananias, with his wife Sapphira lied to the Holy Ghost during a revival, this was so scandalous that God killed them himself on the spot (Acts 5).

Because Christians are declared righteous and objects of God’s love I do not like to use the world punishment, for when a loving father chastises his beloved children to help them grow, this is different from a penalty for the sake of justice such as one serving time in prison. Punishment is still a valid word for many loving parents ‘punish’ their children in this way, but I am just saying God’s vengeance can never touch his people as Christ removed it all on the cross. In this sense death and suffering has lost its sting:

“Death is swallowed up in victory.” “O death, where is your victory? O death, where is your sting?”

The sting of death is sin, and the power of sin is the law. 57 But thanks be to God, who gives us the victory through our Lord Jesus Christ. (1 Corinthians 15:54-56)

There are differences among the denominations, but generally speaking, worldly suffering is not believed by Christians to be punishment for sin.

There is no definitive explanation for why God allows (or inflicts) suffering. But suffering is clearly not related to sinfulness or "righteousness".

As a note: I am non-denominational (just a Christian).

I think there is a difference between Israel and the other nations. Other nations did not make an oath in which they agreed to be cursed if they did not keep all the commandments of the Torah (Lev. 26:14). However, Israel did (Deut. 27:26).

As for humanity in general, Jesus said (Matt. 5:45), "That you may be the children of your Father who is in heaven, for He makes His sun to rise on the evil and on the good, and He sends rain on the righteous and on the unrighteous."

There are some terrible things that happen to pious Christians, and sometimes generally "bad" people get through life "unscathed." I don't necessarily believe that bad people suffer more on Earth than Christians. But, at the last day, there will certainly be a different fate for each.