I had to go back and read some of your previous posts to figure out what kind of camper you have. In a previous post you said you have a Coachmen Clipper 17RD (For visual,
Click here.)
It's a single axle trailer, which means any weight you add on the back will be noticeable on the tongue. But maybe the trailer is still heavy enough on the tongue, this will not be any issue. Still, this would be my first concern. When the tongue is light, the trailer will get bad sway. But you won't know until you try and see how the extra weight on the back handles.
Next, looking at the many photos on the Google search, it looks like your bumper is a traditional 4 inch metal bumper welded in 2 places to hold it on.
Carefully look at the actual welds and see if the weld runs the entire length of the connecting points, or if it is just spot welded. If spot welded, the bumper will not hold anything but itself. I'd even remove the spare tire in that case.
If the weld is solid along the seam, it will be a much stronger weld and you may have a good chance at success. However, there have been stories of bumpers falling off due to too much weight and inadequate welds. Definitely re-inforce the bumper with additional support before you try adding the extra weight. If it's originally spot welded, have it welded completely. That's an absolute given, must do!
One thing you have to remember, the bumper may be able to support your 200 pounds by simply standing on it. But, if you start jumping up and down on it, what happens then? When driving down the road, the rear of the trailer extends beyond the axle several feet. In the middle of the trailer, bouncing may be only a couple inches. But extend that to back, and the bumper may be moving up and down, being jerked 6 inches to a foot. And the harder the "hit" the more force there is on that bumper. Add additional length and leverage with the carrier hanging on the bumper AND the weight of the generator, and a simple 1 inch bump in the road (could) cause a couple thousand pounds of force bouncing up and down on that bumper.
Bottom line.... yes! Get it strengthened and give it a try. If tongue weight is reduced too much, shift weight inside the camper to compensate.
If it were mine, and I wanted the generator, I'd do the extra welding and support in a heart beat!