You sure the trailer brakes aren't stuck on?
lol
but seriously, if it accelerates really well without a trailer I'd be worried about the trailer. If you think that the extra weight of the trailer is just causing an existing problem to surface then mess with the truck
My IP died at 129k miles. Started spewing fuel out the weep hole. I just put on a re-man stocker. I don't drive much, have 130k on the truck now, still have stock injectors. Seems to pull just fine (I usually pull a 20x8' box trailer full of motorcycles, only 4k lbs or so, but pushes a bit of air).
Certainly have no trouble getting over 65 or 75 for that matter.
Do you get any black smoke when towing with the peddle to the floor? Do you have boost and pyro gauges? (if not, you'll need them before installing kens stuff).