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As a very similar TV weight reference point; I have a 2016 Silverado Double Cab, LT, 6'-6" Box
, 6.0L, 4:10 ..........., my CAT scale weights with, 200lb driver, full fuel, 250lbs cargo (no passengers):
Steer Axle: 3,940lbs (5,200lbs GAWR)
Drive Axle: 3,180lbs (6,200lbs GAWR)
Gross Weight: 7,120lbs (9,500lbs GVWR/per door sticker)
My available payload capacity
: (9,500lbs - 7,120lbs) = 2,380lbs
"If" I had the 8ft box (like your 2500HD) the CAT weights would be a little heavier, not sure if the GVWR would increase to 10,000lbs (in lieu of my 9,500lbs), check your TV's door jam.
I tend to agree that your 2500HD will not have enough available payload capacity for the 315RLTS. Figure a FW "loaded" pin weight of 20% (up to 25%) of the FW's "loaded" gross weight.
Take your TV under loaded conditions to a CAT scale and weigh it...., working with "your" real TV weights eliminates the guess work when looking for a compatible TT or FW.