My overhead door sticks at very beginning of open cycle
If your weatherstripping was installed firmly to the door, the problem is probably simple static friction. In total, the seal creates a substantial drag on the door, which is enhanced by warm weather making the seal softer and stickier. 

I'd try applying a drying, not-greasy lubricant to the weather stripping--silicone or Teflon. Alternatively, adjust the depth of the door rail brackets slightly to reduce the pressure of the door against the seal.