How did tobacco affect the English colonies economically during the 17th Century?

Question #1:
How did tobacco affect the English colonies economically during the 17th Century?

Tobacco began to be exported from Virginia in 1614 by planter John Rolfe. It was popular in Europe as a way for the wealthy to display their opulence. It is said, Tobacco saved the colonies, because Tobacco was the first lucrative export from the colonies. It permitted the colonies to purchase goods and supplies from abroad, and made early Virginia a financially sucessful enterprise; however, as colonies grew, the importance of Tobacco is generally overstated. Tobacco was only grown in 4 of the 13 Colonies. Primarily Virginia, but also southern Maryland, Deleware and parts of what is today North Carolina. Economically it was important for Virginia and Virginia was the largest most economically successful of the thirteen colonies; In the majority of the 13 colonies tabacco's importance was only tangential.

Question #2:
I'm curious as to how tobacco affected the colonizing nations economically.

Tobacco was a labor intensive crop. Like Cotton, it's cultivation as an export crop always was dependent upon slavery. As Tobacco was the first lucritive cash crop for the colonies it was also the first crop to demand the mass importation of slaves. That is the real economical impact of Tobacco for the colonizing Nation / Britain. The slave trade ,first nececitated by the cultivation of tobacco, from the late 16th to early 19th centuries ultimately became a foundation of the British Economy, and it all started with the cultivation and export of Tobacco.

Sources:

• John Rolfe
• Tobacco colonies
• History of Tobacco
• Triangle Trade
• Economic History of the United Kingdom

Very much indeed.

Early English Tobacco Trade

While tobacco was known in England definitely from the time of sir Walter Raleigh, legislation seems to have taken some time. King James I, amongst other European monarchs, is recorded as focussing on the law, including issuing a ban against tobacco while the population came to think that it was both popular and healthy:

Many found the breathing in of smoke to be peculiar at best and possibly dangerous. Others objected to being exposed to smoke created by the tobacco user. King James I of England issued a strongly-worded description of his disdain for tobacco and smokers, the Counterblast to Tobacco published in 1604. ...

Thus, against the wishes of many European monarchs, tobacco usage continued to grow, fueled by a belief in its curative powers, encouraged by its general social acceptance among the upper classes, and helped by its importance to the American and European economies.
_{—Young, 'The History of Tobacco and Its Growth Throughout the World'}

Improving Virginian Tobacco

This was overcome by the king's shortage of money which prompted James I to reverse his laws, and to tax tobacco alongside turning its trade into a royal monopoly from 1615 onwards. Originally, however, the colonies didn't produce tobacco of very high quality compared to the Spanish-grown variant:

The first known shipment to England was made in 1613, but was ill-received, the Nicotiana rustica that was native to Virginia being decidedly inferior to the tabacum that was to be had from the Spanish plantations.
_{—Gabb, 'Smoking and its Enemies: A Short History of 500 Years of the Use and Prohibition of Tobacco'}

After the Virginians realized they could make considerable sums off tobacco, they improved their crops:

...with the replacement of the poorer with the better strain, the conquest of the English market rapidly began. In 1616-7, Virginia sent 2,300 pounds to London, compared with 58,300 Spanish pounds. Within two years, Virginia was sending more than 20,000 pounds. In 1620, 40,000 pounds were imported. As the trade increased, the colonists made both mercantile and political allies in England; and effort was soon diverted from the suppression of all tobacco to the promotion of Virginian tobacco at the expense of foreign.
_{—Gabb, 'Smoking and its Enemies: A Short History of 500 Years of the Use and Prohibition of Tobacco'}

Jamestown

Jamestown is brought out as a special good example for how tobacco affected the settlement's development:

Through some very meager times, the English company that founded Jamestown kept it going with food and supplies as the colonists worked on the development of useful and marketable exports. Then, in 1612, John Rolfe, an Englishman and the future husband of Pocahontas, planted seeds of a West Indian variety of tobacco that flourished and produced tobacco stronger and sweeter than the short, tough variety previously grown in the area. Small amounts were sent to London and a tremendous demand grew for the new Jamestown product. By 1617, production had begun in earnest.

In 1617, Capt. John Smith . . . wrote that the colony's new governor arrived to find "but five or six houses, the Church downe, the palisades broken, the Bridge in pieces, the Well of fresh water spoiled" but, in a sign of success, "the market-place, and streets, , and all other spare places planted with Tobacco."

Exports steadily increased and demand from England increased more quickly. Jamestown had found its cash crop and the colonies had begun to guarantee their future.

"The discovery that tobacco could be successfully grown and profitably sold was the most momentous single fact in the first century of settlement on the Chesapeake Bay," Joseph C. Robert wrote in his history, The Story of Tobacco in America. "Tobacco had guaranteed that the Jamestown experiment would not fail." (Susan DeFord, p.5-6)

_{—Young, 'The History of Tobacco and Its Growth Throughout the World'}

From Bans to Taxes

In general, it looks as if most European countries attempted a ban on tobacco trade before allowing it due to both popular demand and taxation:

The various German prohibitions were scarcely sooner shown to have failed than they removed and taxes imposed in their place. In Bohemia, within three years of the complaint, mentioned above, about the popular disobedience of the laws against tobacco, the trade was made legal and subject to tax. In 1669, the Elector of Bavaria, financially embarrassed, called the Diet into session and agreed a tax on tobacco, the decree of 1652 being withdrawn. In 1670, the Emperor himself was brought round to the creation of a State monopoly. Soon after his accession, in 1689, Peter the Great of Russia repealed all the prohibitions, associating snuffing and smoking – both learned from the West – with modernity. In 1697, for a down payment of £13,000, he sold a monopoly of its importation and sale to an English stock company.
_{—Gabb, 'Smoking and its Enemies: A Short History of 500 Years of the Use and Prohibition of Tobacco'}