First post, 35" or 37" tires?

[ChrisGTA]

Hello all, this is my first post and I just purchased a used Stealth gray 05 SUT.
I am going to have to replace the worn out BFG's and am planning on going either 35x12.50R20 or up to 37x12.50R20 ProComp Xtreem MT's. Are there any negatives with going up to the larger size such as a noticeable loss in power, brake issues or a major loss of fuel mileage.
I will be towing a 5000lb RV couple of times a month also.

Also, does anyone know of an extension for the reciver hitch? My spare tire prevents me from hooking up to my trailer without removeing it.

This truck has the lux package and I am planning to remove all the chrome items from the outside and change over to black or black chrome and then do carbon fiber on the inside. Also I have been searching without success for a company that makes wheels and exterior accessories in black chrome. If anyone knows where these items can be purchased please let me know.

thanks.