If you were riding the Road Star around the neighborhood, not getting much over 30 mph, and taking a lot of corners, it will feel heavy if you are not use to it.
Motorcycles are self stabilizing. Above a certain speed (about 30mph) if you turn the bike and release the pressure on the grips it will straighten out. The faster you go above 30 the stronger that 'straighten up' force is.
Below 30mph you get in the zone where the bike will turn, but if you release the pressure it will keep turning ( it wont fall over it will just keep going in a circle) unless you give it some throttle to stand it up.
Below 15 mph starts to feel like a bicycle, you sit up straight to take corners, and a big bike will feel heavy.
About the pull to the right, all roads are slightly banked to the right so the rain will run off, so bikes and cars will have a slight pull to the right going straight, esp going slow. If its still there going 50mph, and you are sure you are centering your weight on the seat, then you might need to look and see if the rear tire is not lined up in the swing arm, or if the front forks are bent.
Or take it to a Yamaha dealer and ask a mechanic to ride it, they can tell you if its not right.