Aside from snapping off fish in cover with the jig, the main reason to use heavier line on a jig is to get a good hookset. Usually you want to set pretty hard with a jig and 6lb will tend to snap off on a hard hookset. If you're using light wire hooks and no weed gaurd, 6lb might be ok, but with a regular jig you're going to get a bite at some point where you set the hook and it seems like the fish is on, but they spit it. A good fish can hold a jig in it's mouth so hard that you have to set hard to get the hook in. That's why the heavier line.
I never use anything lighter than 16lb for jigs unless it's really really clear water.