You will find quite few threads here dealing with carrying things on the bumper. They are only designed to carry the sewer hose. Some bumpers are stronger than others but I think 125lb is pushing it. Some have bypassed the bumper and had an actual frame-mounted hitch welded on. That, to me, would seem the most prudent approach.
Alternately, if you don't carry the sewer hose in the bumper, have it cut off and replaced with something that will do the job.
Next item: if you're going to hang 125lb PLUS the carrier and beefed up bumper/hitch, etc. on the back, you'll have to transfer a lot of interior weight forward to keep the pin weight right.
Stu
PS If you bought a 3500 / 4000 Watt generator that is not red or blue, then you'll want to dismount it to run it.