There are not a lot of adjustments available on recent garage door tracks. My brackets are riveted in place except for the radius - it is movable but doesn't do much good for this problem. If you can't adjust the track to be closer to the frame then you need to adjust the outside weatherstrip to be closer to the door. Generally speaking, you should put the weatherstrip on with the door up. Line up the inside edge against the opening. That will put the weatherstrip inside the opening slightly. With the door open, see if the weatherstrip is lined up with the edge of the opening or if it is further out.
Having said that, if it's way off then you may have to install with the door down pushing it in instead of just laying it against the door.
There will always be some movement with wind since getting it too tight will restrict the movement up and down but that seems excessive.