According to Richard Frothingham’s History of the Siege of Boston:
In the last week of July  the number of inhabitants was stated at 6753; the number of troops, with their dependents, women and children, at 13,600. . . .The civilian population of Boston had shrunk to about 40% of what it had been in 1765, the last year for which we have a detailed census. However, that figure included hundreds of people from Loyalist families who had moved into the capital from the countryside since September 1774; over a thousand civilians would leave Boston with the troops in March 1776 rather than stay under Patriot rule.
The troops had an abundance of salt provision, and of fish, but this exclusive diet rendered many unfit for service.
Furthermore, the overall count of people in Boston had grown by a third since 1765 because for each remaining civilian there were now two people connected to the British military. And the town, which normally relied on shipments of food, firewood, and other vital supplies from the countryside, was cut off by land by the besieging Continental Army.
(Thumbnail map above from the Boston Public Library’s Norman B. Leventhal Map Center. Check it out.)