According to Popular Mechanics, answer to a question regarding max tire pressure:

 

I used to run 45 on my original Bridgestone Duelers and got better gas mileage than I do now but the ride was a lot rougher (if you can imagine that) and eventually my tires wore out prematurely in the center of the tread. Basically what I gained in gas mileage I lost in tread wear. Just an FYI.
I now have Kumho Road Venture AT51 tires, run the at 34-36 and they ride very comfortable. They also have about 28K miles on them and still look like new and I'm averaging 16.8mpg around town and about 17.5 on the hiway.
What I've found out more than anything is with the 3.7L engine, gradual acceleration helps a lot and cruise control, whenever practical, is your friend.

 

I agree Chooch. I'll keep a close eye on the tread wear and see how it goes. I am a gentle driver and I use cruise almost always when traffic permits.

 

Holy crap...I know this is going to sound crazy but I just ran another mileage test with around town driving (country roads with 35-40 speed limits) nice and easy and the results are freeking stunning. Before I aired up my tires to 50 psi I would get about 89 miles on the odometer and my fuel gauge would read 3/4 of a tank. I checked yesterday and I had 95.4 miles on the odometer and my fuel gauge was between full and 3/4. I topped off the tank and took on 3.5 gallons of gas. That is 27.25 MPG! I can't believe it myself. I will run another test and see if the results are similar. Yeah, yeah, I know it sounds unbelievable but it's true. If you doubt it, try airing up your tires and see if that makes a significant difference in your MPG. I'll bet it does.

 

Your methodology may be a bit flawed. To try and get the most accurate gas mileage you should fill the tank, don't top it off, just fill it until it clicks off. Run your vehicle until it's down below a 1/4 tank, then refill it again. Record the amount of gas used and the miles traveled. Do it for 3 consecutive tank fill ups and take the average. This will best replicate what you will experience during normal driving, which is what you really want to know. Also, you will see a difference if you do this at different times of the year as your Hummer will run different in colder weather than in warmer weather.