Hello, welcome to JustAnswer.
Did you look to see if the throttle lever it's self, has a tensioning screw on it? Some of them do. It would be accessible from the bottom of the handle its self. If you see a notch or a hole in the very bottom of the moving part of the handle, That is where the tensioner will be. It will likely be a Allen head.
Adjusting the tension at the throttle arm on the motor is kind of frowned on. It takes away from the motors ability to return to idle should the throttle cable break.
No sir, I don't think yours is adjustable.
Does your control look like this one? If so, nope, no tension adjustments. You can come on back any time.
Does the throttle get pulled back completely, or just a little bit and then stop?
No, there isn't. And unfortunately the controls are not upgradeable. You would need a complete unit.
I went down and checked one out after another expert mentioned some success with it. I have to say it really looks and feels like a good design. I will suggest it to the next customer that comes to the shop with this problem, to be sure.