you add more pix.. by simply responding to your own post ...

not a great pic ...

trees basically NEVER stop growing.. pruning.. or not pruning is not going to change that fact ...

second.. with the lack of focus i cant tell why they are leaning.. if they are doing it.. trying to grow out of the shade of the house or some bigger tree.... they will NEVER grow straight up ...

i cant tell about pruning.. until i see an in-focus pic

and if they have to lean... of which is one of the reason to plant birch in the first place... make sure they dont lean TOWARDS the house... that would be the ones i would be looking at for removal ....

ken

I agree with ken_adrian! I'm having real issues with my River Birch trees that we planted about 11 years ago. They are totally out of control and very large. One is also leaning toward our house (due to a nearby Pecan tree). I don't think I would plant that variety of tree too close to my house again. They are lovely and do grow fast, but they can really get out of hand. We trimmed low-hanging branches for years, but the tree itself just got bigger and bigger.
Good luck to you! I hope you find a way to prune them suitably!
Also, beware of their root system because they are very "rooty" fellows! It may not pose a problem if your house is not built on a concrete slab, but otherwise, the roots can cause problems there too, as well as creating issues with your lawn.
In retrospect, River Birch trees are lovely for a far end of a yard, but perhaps not too great up close to the house.
It may be that if you are in a cooler zone than 8 or 9, the trees won't grow as fast. In Southern South Carolina, they grow like mad!

This pic may be a little better. There's really no other trees close by that are causing shade issues.. and my house is only a one story and doesn't really block the sun either.