I don't use WMP so this is only a thought; are there setting within the program itself?
Or, what happens if you re-size the window; close it; then open it back up again; did maximize again?
There's a neat little utility called ShellFolderFix for Windows 7 the will cure 7's amnesia regarding window locations and sizes. Try that.
It works great for me and you can get it here: ShellFolderFix Remembers Window Locations in Windows 7 - How-To Geek
Good Luck!
My Computer
At a glance
Windows 7 Home Premium x64AMD Phenom II X6 1600T16GB PC3-10700 (1342MHz)ATI Radeon 5770 HD (x2) CrossFire