About the only jighead I've ever put on a Carolina Rig was a floating jighead, to stillfish leeches or minnows. I've never used a jig on a Texas Rig.
If you want to add weight to a jig presentation, use a Wolf River Rig (a three-way swivel). Tie a light jig to a short leader on one loop, and either a heavier jig or a bell sinker to a longer leader on the other loop. Personally, I'd go with the double jig set-up, because you can get a fish on either one... maybe even both! Another thing you can do is add a splitshot about a foot or so above a single jig. But as far as jigheads on a Carolina or Texas Rig... I don't know. It might work. Stranger things have happened. Tight lines and slimy nets, man.
If I'm not fishing, I'm thinking about it.
Keep the line fresh, the hooks sharp, and have fun fishing. God bless you. -Sonny, Life Member since 2002