You fall in that tweener category, with experience, at least on BMX but smaller in stature, so I'd say a Honda CRF150r. This is a four stroke that is not as big or fast as the 250cc's but has a lot more power than the "trail bikes", TTRs, DRZs, etc.
go sit on some .. take a look at the 300- 350's .. but most bikes are tall, the weight is a non-issue, the height may be depending on what your comfortable with, hanging off the seat to stop ect .... straight up if i held the handlebars while you sat on alot of bikes, your feet would be dangling about 1 foot off the ground ..
Depending on your funds, a used KTM, BMW, Honda, Kawasaki or Suzuki would work well for you. Go and try them on for size, any of them will handle your weight and size!
I think KTM exc-450 will be good