I totally agree with skyhighsami.
You're running a pretty short tire, only about 30.7" diameter. However, those 22s are pretty heavy compared to the stock 16s or 17s that were on your Tahoe.
Don't bother with 4.10... It will be an improvement, but probably not worth the expense. If you're going to do it, go 4.30s.
Right now with your combo (275/40-22, 3.73s) you should be running about 24 mph at 3,000 rpm in first gear. With 4.10s you would be running about 22 mph at 3,000 rpm in first gear. This means you're getting into your powerband sooner, which means less throttle and likely an INCREASE in fuel mileage. However, this change will be very, very small. Not worth the time or money of swapping gears.
Also, with your current combo you should be running about 2,150 RPM at 75mph. If you would jump to 4.10s, you'd only jump to about 2,350 RPM at 75 mph. That will cause a negligible difference in gas mileage on the highway.
So, upgrading to 4.10s from 3.73s? Not worth it in my opinion. It will be better, but not enough to justify the cost/hassle.
I would, however, recommend upgrading to 4.30s!
In first gear at 3,000 rpm you'd be running just under 21 mph. That's over a 3 mph difference from your current setup...you'll be hitting the powerband much sooner so that means better acceleration and you'll need less throttle to do the same amount of work which SHOULD equate to better fuel economy--if you can keep your foot out of it! Haha!
Also, with 4.30s you'd be running about 2,475 RPM at 75 mph compared to 2,150 RPM currently with 3.73s. If you're doing a whole bunch of high speed interstate driving this will probably hurt your mileage a bit, but I'm not sure how significant the change will be....