Like mentioned above, ther are a lot of variables to look at. The main thing to consider is where and how are your bites happening. If most of your bites are coming on the fall, then usually going to a lighter head or bulkier bait, to slow the fall will get you more bites. However, if most of your bites are right on the bottom, you will usually be better off with a heavier head. It will cut down on the dead time of you waiting on the bait to fall to bottom.

Also, in my experience, if fish want a bait fished slower, then I will downsize my bait, but increase my weight. IMO you can fish a bait slower with a larger weight. A lighter weight will tend to hop further off the bottom and glide further before coming to rest again. A heavier weight will bounce up and fall right back down, keeping the bait in the strike zone longer.

It all comes down to analyzing every bite to determine which method is producing the best. I usually will have 2 or 3 jigs and the same on shakey heads tied on at any given time. I will experiment with the same baits to see which weight of head will get more bites.

Also, heavier heads are much easier to fish in high winds.