The charts from GM has the GCWR change with only diff ratio...also their MTWR also increase with higher numeric diff ratios
Here is a RAM 2017 half ton ratings chart...all OEM's used to have these that shows or compares the GCCWR & MTWR vs diff ratio
For some,depending on the diff carrier, going from 3.73 to 4.55/4.88 might require a carrier change. The diff pumpkin remains the same.
That would also mean changing the G80 locker, if you have one. I'd go with a Detroit locker with no clutches.
Agree with Burbman about going to a GearVendors OD. It replaces the tranny tail housing and no driveshaft changes needed. Ditto if 4x4. GV has a 'splitter' option that will automatically shift in between each 4L80/4L80E gear. Turning a 4 speed automatic into an 8 speed automatic. Still noodling whether a GV 0.5 or 0.75 OD. Think an 0.5 is too close to the HP required to cruise at 65MPH and it might hunt...so leaning towards 0.75
Also, check your wheels to make sure they are +3,000 lb rated. Mine are 16x10 (bead to bead) rated 3,200 lbs. Get concentric if you can, otherwise they will be lug-centric. Both okay...just that concentric is better of the two.
That is in my list of things to do to my GMT400, 1996 K3500 Suburban.
Yes, still an older 'truck', but that is a personal choice thing.