All of the Tomos mopeds I've seen will hold up to 300 lbs of big guy.
However, alot of weight can mess with speed and performance on most vehicles. You might go with Tomos, or you might look for a light motorcycle or trail bike, which has more power to it.
The Honda CT90 and CT110 are not too much to handle, and will carry your weight with ease. However, they might not be "street legal" in all areas, as they were designed for country trails and offroading. Nevertheless, they are built very much like a moped.
In general, you are right. Most of the stock mopeds and scooters these days are built for the skinny college kid or teenager. I've been shopping for a moped for almost a year now, and am about your size. I'm likely to go with the Vespa Ciao, an older moped, or a Vespa PX125, which is a scooter. Something to consider, just because the spec sheet says 250 lbs., doesn't mean it won't hold 270. As I mentioned above, weight affects performance. If you can find a spec bike with weight maximums similar to your own, you can probably ride it at reduced efficiency. You shouldn't expect to zip around on a moped anyway.
But, try to avoid that if there are any other options, exceeding performance limits by too much will put wear on the engine.