Yep, weight is the big issue with turning a utility bed into a trailer. I've seen several write-ups that did so and that seemed to be the one significant drawback to having all that convenience.
If you look long enough, you can find utility beds for virtually any cab-chassis platform. The ones for small trucks are generally more scarce, I suspect in part because the limited capacity is much more of an issue with them.
I have seen various fiberglass or plastic utility beds in recent years. One of those would be ideal for a trailer, as it would be much lighter. Thing is that they don't rust and are more expensive than metal utility beds, so people hold onto them or transfer them to a new truck.
1997 FZJ80 The Sacred Cow 152k, 255/85 R16 BFG KM2 on 16x8 Toyota Steels Rims, ARB w/ XRC12, dual batteries/Hellroaring isolator w/ Blue Sea battery switch feeding winch and dual inverters, CDL switch w/ 7-pin mod, cupholders!, 8-ton pintle hitch w/ GI chain plate, blue-PHH, working power antenna, FSM, camper conversion
M101 CDN Tagalong to the boonies, 255/85 BFG KM2 on 16x8 Alloys, w/ custom extra wide fenders, fresh OD paint, bungied tarp and bows