No you shouldn't have any issues as long as you stay with a zero offset rim. What stresses bearings is wider rims that move too much of the unsprung weight outboard and create leverage on the bearings.
If you go to D rated tires be sure the rims are rated for 65 psi, or 80 psi if you go to E rated tires.
Be sure to check clearance above, you want at least 2 1/2" to 3" above the tire to allow for suspension travel. You may need to "flip" the axles if they are over the springs now, or add spacer blocks for increased ride height.
Also remember that raising the TT will also mean readjusting the height or your WD hitch and dialing in things again after the new tires are on.
I went to LT tires 2 seasons ago and had to lift the suspension 2" to get the clearance I needed, and also had to go from a 2" rise stinger for the HA to a 4" rise to keep the TT level when towing. All in all a worthwhile mod, and would encourage you do it if you can, you can't have too much extra capacity on these tires.