The most common way for a spinnerbait to become heavy in the water is to become foul with weeds. While spinnerbaits frequently can make it through and around larger weeds such as lily pads, the smaller weeds such as hydrilla will catch and accumulate on the hook and body of the lure, making it cumbersome until you remove them.
When you attach your spinnerbait with a swivel to your line, the lure may slip through the swivel from where it normally sits. This will make it feel different as you pull it through the water, as you will not have the lure centered. You can quickly fix this problem by simply centering the spinnerbait in the swivel, or eliminate the swivel and tie your line directly to the spinnerbait.
Sometimes when you cast, the spinnerbait's own hook can entangle with the small circular "eyes" that attach the blades to the lure. Once this occurs, the blades will not spin properly and the lure will have that heavy feel as you bring it back to your position.