I'm confused as to why this was a point of contention for the colonists. Did your average Massachusetts or New York farmer ever actually encounter these troops? Why were they bothered by British troops being stationed there, if they were on the same side?
Look up the Quartering Act of 1765. A similar act was included in the Intolerable Acts of 1774.
Troops' expenses had to be paid by the colonists, rather than by the Crown. Soldiers had to be housed and provided with food:
V. Provided nevertheless, and it is hereby enacted, That the officers and soldiers so quartered and billeted as aforesaid (except such as shall be quartered in the barracks, and hired uninhabited houses, or other buildings as aforesaid) shall be received and furnished with diet, and small beer, cyder, or rum mixed with water, by the owners of the inns, livery stables, alehouses, victualling-houses, and other houses in which they are allowed to be quartered and billeted by this act...
The food requirement was dropped in 1774, but soldiers were still to be maintained by colonists rather than by the crown, and colonists still had to provide soldiers with housing. It was also a violation of the Mutiny Act of 1756, which had placed restrictions on quartering.
If tomorrow four US soldiers showed up and you had to give them a place to stay in your house, wait for them to shower in the morning, cook dinner for them, and so on, the fact that they were your own country's military wouldn't soften the blow much.