a few things
As RevvinKevin said, caution with that fill flume as you lift the top. Once you get the hang of removing it from the flexible plastic/rubber guard, no problem.
The fill leak------check in rear left corner, from where hoses screw on to the back of the machine, all the way to where it shoots into the tub. Any/all of these parts are replaceable, there should be a short hose from the valve to the side of the tub, then a vacuum break plastic assembly, then the final nozzle into the tub.
Spin leak----during the last half of spin, it spray rinses, so maybe you are leaking each and every time it fills.
OR---the top of the entire machine is also the top of the outer tub. During the first part of spin, with even just a half load of water, the water runs high enough up the sides to go over the edge of the tub. There's a rubber seal all the way around the tub top, should be tightly pressed against the machine's top underside. Check all around that, see especially if you can find water drops running down the outside of the tub. When fully loaded, spin creates a hell of a lot of water right up against the lid, by design. Whenever I am all the way done working on a Filter-Flo, no more opening the top for months, I use Vaseline around that rubber gasket. With all the ridges it has, I figure the Vaseline won't all wear away quick, can help that last ridge or two against the few drops that make it that far. But that is after making sure that it seals well around the flume, against the clean dry lid, etc, no cuts or breaks.
A fill leak or spin leak should be easy to find, diagnose, repair. GE's are good machines. It always helps to watch in use, see exactly where/when the water comes from.
