I currently have 400# Equalizer with the Roo 19. It has a dry wt of 3383 lbs, a GVWR of 4770 lbs, probably runs <4000 lbs down the road. I have had no problems or concerns with it.
The 2503S is coming with a 600# Equalizer. It has a dry wt of 4310 lbs, a GVWR of about 5363 lbs (4310 dry + 1833 cargo), and I expect it run <5000 lbs down the road. I'm not expecting any problems.
My Silverado has a tow capacity of 7500 lbs. Of course, payload is an issue to be aware of, too. On the Roo 19, with a dry hitch wt of 446 lbs, plus some down the road (the WDH and cargo), I'm still good on payload (just the DW and I). I'll still be good with the 2503S.
A word of caution: Anything anyone tells you about the capability of a 1500 you need to take with a grain of salt. My Silverado's owners manual lists 99 (yes, 99!) different permutations of the 1500 (different engines, trannys, rear ends, HD equipment, std cab, extd cab, crew cab, etc.) The towing capacity of these 99 permutations ran from around 4800 lbs up to about 11,000 lbs (I've quoted the exact #'s in other posts). That's quite a spread. (Keep this in mind when that RV salesman tells you "Oh, sure, a 1500 can pull this trailer!" Well, maybe it can and maybe it can't!)
Bottom line: You need to know exactly what the towing capacity and payload is for the TV you intend to use.
All that being said, it SOUNDS like you'll be OK as you have more tow capacity than I do and I'm not worried.
Of course, I haven't pulled my 2503S yet, either. Ask me again in a few weeks!