Although the gravitational pull is the same on two jigs of different weights, the frictional coefficient of water is far different than air which makes the fall rate different for each jig... this is essentially a parallel demonstration of the hammer and feather on the moon.
To prove it to yourself, experiment with identical skirts and trailers on a 1/8oz and a 1oz Poison Tail (or any other jig with a notable weight mismatch); we cannot discern any real difference in speed as they fall through the air, but there is quite a noticeable difference as they fall through the water.
It will take a lot to replace the notion of "going with the lightest jig possible" that dear ol' Dad drilled into my noggin, however I do think there is something to be said for the reaction strike of a fast fall (and I will experiment with this come ice out).