When it was smaller, I left three main branches as it didn't give much privacy without the extra foliage and branches. It's now bigger and I should probably correct the problem I created. (Or just cut the stupid thing down and replace it. That may give me even more headaches as the previous owner planted it quite close to the gas line)

With three main branches shaped like a three pronged fork, I'm asking for trouble, as it causes weakness, correct? The outer two are about 7 inches in diameter. I should cut them completely off this spring and the main trunk will continue to branch out further won't it? Or have I created a narrow tree for myself?

Cutting off that branch should work also, I find they readily shoot out from the trunk but need to be patient a couple of years.
I find chokecherries are prone to grow branches as you say
[three pronged fork], I have tied some down when young,
I might not worry too much,..if left alone, because they seem to be very strong.