Someone on another forum was looking for a scooter for the same reasons. He wanted two up, haul on RV and under 300 lbs if possible. The scooter he ended up with was a Sym HD200. It's slightly over 300 lbs but will handle 2 people and tops out at 70MPH+. If you can find a used Kymco Yager 200 it has similar performance and 2 people should fit.
I have done quite a bit of 2 up on my Aprilia SPort City 250 but it's around 350 lbs wet.
As you can see the seating is a bit tight. I'm 6-2 and my wife is 5-7.
Another pic just because I feel like posting it:
The Sym HD200 and Kymco Yager 200 seem to be about the same size as my Sport City which is smaller than most 250cc scooters.
I have sat on a Like 200. The seating position seems cramped for me but the seat should be long enough for a passenger.
Another thing to consider is the suspension. Both my Super 8 and sport city have stiff suspensions so they handle a passenger well. A small scooter with a softer suspension may not.