Last time out, I used a 3/4 oz jig head with plastic and a floating jig head with a minnow on my Dubuque rig fishing downstream, and in minimal current areas both up and downstream with some success. I tried to slow the boat just enough going downstream in the current to have a slight angle to the line going downstream. All of the fish were caught on the floating jig head and minnow. Not sure how much weight would have been needed to fish strictly up stream under the same conditions, keeping the line angle minimal, and actually making progress upstream instead of falling back. I would guess it may have taken a 1 to 2 oz jig head.