quicktime movie window position an size

What to do to solve this problem?

QT media players always open the file at the "Current Size" setting embedded in the file. If you have never reset this value, it is normally initialized to the same value as the "Normal Size" (original encoded anamorphic or non-anamorphic display size). Most QT 7 users who have keyed their player for "Pro" use would simply change/save this value to reflect the resolution at which they want the original file to open or create a "reference" file with a different desired opening resolution. Otherwise you will have to manually reset the display size each time you open the file just as you are already doing.

If I don't needed quicktime for GoPro I never installed it,there are so many players for free as good or even better than quicktime that automatically give the right view,no matter what the resolution of the movie is.

Then why don't you use one of them. Since you said your files contain H.264 video rather than one of the Apple proprietary video codecs and since QT only plays data encoded to the JVT standard, your GoPro files should be compatible with any H.264 capable media player. The only advantage to the use of the QT player is in those instances where the file contains embedded settings which are only read/used by the QT player and ignored by third party players.