Getty - I'll second the vote for the Lance 815 Lite as one of your lightest, fully self contained TCs. They don't make them anymore, but there are still some great, clean ones out there.
As a reference, I have a 06 Chev 2500HD 2wd, and a Lance 835. I bought it because I too have a trailer and didn't want a hitch extension - the 835 doesn't have an overhang so it works great. The 835 full of water, linens, silverware, pots/pans, etc., everything BUT food, weighs 2,250 lbs. I looked around for my scale ticket, and if I find it, I'll post it, but with my 245/16 load range E tires, I have 600#s left for provisions and tongue weight on my rear axle. If I had 265/16s, I'd add around 800#s for a total of 1.400# additional tire capacity, but will have hit my rear axle rating at about 1,000# over my current truck/835 load out.
I also have a steel deck trailer that is as much a 7,000lbs fully loaded. With my current set-up, I cant do the trailer and the camper with anything more than about 4000#s on the trailer, or I'll hit my tire limit. New 265/16s would allow me to max out my trailer too.
An 815 Lance Lite weighs approximately 200#s less than an 835, so with 265/16 tires, that may just squeak you by with the 1000#s of tongue weight you'd need to have for a 10,000+ pound trailer.
Do your homework carefully and I'm sure you can get where you want to go. But you will be right at the max limits in many areas; tires, axle, MCGVWR, etc.
Good luck.