I used to work in the car industry so I know a little about tires and wheels. Stickon wheel weights do tend to fall off. They aren't meant to be permanent. All of your tires are probably out of balanced right now by a few ounces each. That just happens with wear.
If I were you, I wouldn't do anything until you feel vibration at high speed. That indicates that your tire(s) are out of balance. It might not be as noticeable in the ear as it would in front. I wouldn't waste the long drive to the dealership unless you feel this vibration.
IF you decide to have your local shop do it, make sure you tell them to do a tape weight balance. That might cost $10 or so. If you don't tell them, they MIGHT do a standard balance and put weights on the outside of your rims and scratch it up .