How many cc engine do I need?

I'm new to motorcycles. I'm 6'4 and weigh 350 pounds. My Girlfriend weighs around 150. We will normally be riding it together so I need a motorcycle that can easily handle 500 pounds on it at highway speeds. I'm interested in the Honda VTX 1300. Would that be enough? Could I go with a lower cc engine and still handle 70 mph easily enough with 500 pounds?
Added (1). Would a 750 cc engine be enough? Also considering a shadow aero that I'm looking at. I like the Honda's and I hear they are reliable.
Added (2). I'm looking to spend as little as possible because I do not have much money to spend right now, but other good motorcycle recommendations are welcome.

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