Where your strong, where you weak. The gym is self quality time. Another added benefit is that it reduces the amount of recovery time needed. A body that has stronger muscle is also more responsive. As your body gets into better shape you will find it follows your commands quicker, becoming more responsive.
Muscle does what it is told to do for as long as it can do it.
Fat just hangs on you body like a dead albatross. That is not to say some fat isn't good. We're not trying to be bodybuilders here. Simply remember that the goal of lifting for grappling is to become stronger. Sometimes when I talk about weightlifting people summon of visions of bulging roid boys who cannot put their arms together.