I asked the question at a fishing seminar years ago.... When do I throw a specific weight of a jig?
The answer was it depends on ROF, depth, temperature, etc. Basically what has already been mentioned above with one exception. Water clarity as it pertains to what the bottom is made of. What he was saying is that if you have a muddy or sandy bottom and big jig, a bass might avoid it as it stirs up more stuff. Just like us, they don't want to breath/suck in a mouth full of mud and sediment. So go small, be patient, and make smaller movements with the jig.
This why I take both a 1/4 and 1/2oz jigs with me when I go jig fishing. In the summer, when it's hot and there is a lot of vegetation, I might go smaller and heavier with a 3/4oz for weeds and lily pads and a 1/8oz BFS jig for shallow water. When none of that maters, 3/8oz for everything.