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For your size and weight, I would say that the GZ is too small in the power department and the fit department. I'd suggest an Ex250 (Kawasaki Ninja 250) Or a Honda Nighthawk 250.
Check out the member pics for an idea of fit. I'll post the pics below. I'm 5'11 and I fill the bike up. Any smaller and I would not have purchased this bike.
Also, at 270 pounds, you're going to find it difficult to get this bike to zoom you along. I fill it up at 5'11 but I'm a light middle-weight.
The Ninja 250 has the power that you need and the taller seat height will make up for the lack of leg room that you will have on the GZ. It is also very forgiving to learn on. I know. It was my first bike.
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