I think most of the 200 and 250cc class Chinese dual sport style bikes are less than 300 pounds.
It sounds like what you want is one of those, and a
hitch mounted motorcycle carrier. Or maybe a TW200. Or a Trail 125.
Edit to add: My usual blurb about hitch carriers. If you're going to use one, be incredibly mindful of your hitch AND VEHICLE'S tongue weight capacity. This is not the same as tow capacity. Whichever value is lower is the one that counts. The entire weight of the bike and the carrier is suspended in the air on the hitch. The thing is also flapping around like a diving board, acting like a lever on your hitch and its mounting points every time you go over a bump, etc. The tongue weight limit on most unibody vehicles, for example, is typically no more than 250 lbs. And it doesn't matter what the rating of the hitch itself is, because it's still attached to your vehicle somehow, and beyond that rating is when it gets ripped off...