With abundant food and no real competition, beavers can breed fairly rapidly. I've heard of beavers wandering long distances as well looking for new areas, so the population could very well stay steady in your area.
I've seen 3 beavers in one area before, one was very large, the other two big, but noticeably smaller, so it is probably all in the family unit.

I'm sure the trapper appreciates the opportunity to trap on your land.