I had the same problem on two different sets of rubber and chrome grips. I found a solution that fixed the problem for good. I switched to leather grips. I love them.
Stoners trim shine. Some O'Reillys parts stores have it. It also works great on all the outside plastic parts on a car or truck. It's different from any other type of plastic or rubber treatment. You just need to find it and try it. They also make a great glass cleaner called Invisible Glass.
Most grips for bicycles are designed to be sticky, I assume that they are the same way for motorcycles. The hotter it gets the stickier they get to help you hold on to them. Mine does this and during the summer I have to use very little grip pressure to hold a constant throttle position. Slick grips and wet hands don't mix. It is a diffrent story if the sticky is coming off on your hands, that would mean they (the grips) are breaking down and need to be replaced.