I replace the tires with Cooper tires and they are wearing great.  They were a little squishy at first, but that was because I was comparing them to the rocks that were one the truck.  I am used to them now and like them a lot.  I run 50 in all four, unless pulling my equipment trailer or hauling something heavy in the box, then 80.

When I do get new tires on my car or truck, I have them do an alignment.  They may be able to tell you as they do all four wheels.

Also, rotate your tires.  While I'm guilty of not doing that as recommended, in your case you will extend the life of all the tires, instead of just burning one up.

My thoughts,

Carl

With it on level ground,lay a level on the wheels and see if they are standing straight up.

 Had a 76 chevy one time that the axle tube was bent.

 A 4 wheel alignment machine would be a good diagnostic tool.

Carl

 We try to be easy on the Chevy guys. They have enough problems without us bothering them!

Regards,

 Chris

I picked up a 2007 2500HD 2WD cab & a half short bed with over a 100K miles for use on the farm some years back and it sat for over a year in the shop until I had a new CM bed put on it for general use including gooseneck trailering. Always bugged me that it had a slight "clunk" when leaving a light and my fear initially was a worn out rear as uni joints were tight and lubed. Called a truck suspension shop in Fort Worth, relayed the symptoms and he chuckled before telling me that if the rear end was not clunking by binding on short corners, "run it as that GM rear will likely outlast you". Advised the spring mounting bushings were likely worn in and the GM's were known for this.  Ran it by a friends shop for him to watch the rear when put into drive from park. Sure enough, you could see a small amount of play in worn bushings and he advised he had seen many do it and GM eventually changed out the material for these bushings. Had me view it while he moved it from park into drive and then asked me if I ever felt it with the stock trailer or flatbed  gooseneck or bumper pull trailers hooked up, even empty. I realized then that it was less obvious after installing the flatbed as it was heavier than the stock bed. Picked up 10 sacks of feed (500#) on the way home and sure enough, just enough weight to get the rear springs in a little bit of tension at the bushing area and no noise made at all. Same with any of the trailers as just the hitch weight takes care of it.

Have monitored/rotated the tires throughout as nearly new when I bought it and they have worn evenly and normal wear with over 50K miles now.

Only thing I have done is add a can of BG to the rear diff and clear the rubber vent tube so she can breath and she has been on a number of long trips including trailering without issue.

Best of luck on gettin your ol' gal straightened out.