from stock to 37" tires
 

hummerxforums claims switching to bigger tires wouild cause following:
""You'll lose some low-end torque, as you will have effectively changed the gear ratio.
Your speedometer will read low.
Larger diameter tires are usually heavier, putting more stress on the drive line and suspension.
Wider tires may cause a little wandering on the highway and increase rolling resistance.""
anyone had similar experience?
thanks

A little bit, really not enough to matter.
If you do so pull your battery for a couple minutes so that the computer can relearn a new shift sequence since, as you quoted, you are changing the final ratio.
The biggest issue I found was my transmission wanted to constantly shift when cruise control was put 75+. Not so bad now that the trans had time to learn it.

I didn't go above 12.5 width but I would make an educated guess that you'll see more wandering from a loose ball joint than a slight increase in tire width. If it did become a problem I would try changing the steering stabilizer.