Mama to two wonderful boys DS1 (May 2007) and DS2 (March 2011)
The shoulder belt must be coming out of the belt guide at or above his shoulder and the tips of his ears should not be over the top of the booster. I'd be surprised if he's outgrown the turbo by height at 6 1/2. The back probably just has to be raised.
As for backless, it's up to you. My personal preference is when they outgrow the back of their hbb or 8yo.
Have you adjusted the back up? There should be a handle on the top of the headrest that you squeeze and then pull up on--- the back will extend and get taller. A 6.5 year old would have to be REALLY tall to have outgrown the back portion.
There is no evidence that the backed booster is *safer* than the backless--- many people just find it more convenient for napping and reminding their child to sit correctly. If your child sits correctly and the belt is positioned correctly without the back, then he's fine with a backless. Of course, you still need to have a seat back that goes above the ears, so if your car does not have head rests and your son's ears go over the top of the seat, he'll need to stay in a booster with a back.
As for getting out of a booster, you need to pass the 5 step test (this will be quite a while):