Getting below 7# with any double muzzleloader would be tough.
especially in 10 bore, but I feel a 6.8-7 lb gun is doable (especially if you eliminate a loading rod and thimbles on the gun).
A 12 bore with 26" barrels tapering from 1.12" to .805" (each weigh roughly 2.45lbs), Two locks weigh .5lbs, A Butternut wood stock with a cavity in the butt and a splinter fore end should weigh .5 pound. A thin butt plate and simple trigger guard should weigh roughly .25 lbs. A wood rod should be .125 lbs. Barrel keys, breech plugs, and regulating wedge should only weigh .25 lbs together, and ribs should only weigh .125 oz together. That's 6.65 lbs.
A 20 bore double with 26" barrels tapering from 1" to .7" (2 lbs each) would reduce the weight to 5.67 lbs
a little .40 with 26" barrels tapering from .8" to .48" ( each barrel weighing 1.53lb) would weigh about 4.81lbs (that'd be a nifty rabbit gun)
By way of comparison, a .50 double rifle, with 26" barrels tapering from .9" to .75" (2.79lb each) would weigh about 7.33, but if you could control yourself on the heavy loads and were only going to use the rifle for deer and targets, you could shave the barrels down to .85"- .7" (2 lbs each), you'd have a rifle that would weigh 5.75 lbs (gotta add a ounce for sights). You'd just be stuck with heavy pistol loads ( 55gr and a sub 300gr projectile is perfectly adequate for deer within 150yd). Then again, you could get away with a 20" barrel in that "carbine" configuration (so long as you stuck with 3F or 4F for charges) and still gain quite a bit of velocity over a pistol (not to mention the stability of a shoulder stock). a 20" barrel of the light contour would weigh 1.55 lbs a piece, meaning the double carbine would weigh something like 4.9 lbs.
(before anyone worries about the wall thickness, keep in mind that the chamber wall of a Colt 1860 is roughly .050" thick, and that was meant to be able to be loaded with 30ish gr of powder and a 220gr bullet (A Colt Model that came out about 13 years latter was meant to be loaded with 40gr of powder and a 250gr bullet, and it's chamber walls were .045)) Not going to find guns like that from big MFG's, though, they're worried that you'll use a BP measure to volumetrically load smokeless in it and blow yourself up lol.