DME does work for carbing, but you are only adding a fraction of the total fermentables, so it will not increase the body much. The reason it's so thin is the amount of sugar added, which contributes alcohol only and adds no body. Carbonation will change how it tastes. Usually it adds some mouthfeel, so it will only help. You'll get this batch drank up in a month or two and be on to the better unhopped extract kits which will be maltier.
Primary #1: Empty #2: Black Currant Wine
Secondary #1: Berry Rhubarb Wine #2: Empty
Kegged: Cascadian Dark Ale
Bottles: Spruced Winter Warmer, Surly Bender clone, Big 50 Barleywine, Framboise Lambic, Dark Belgian Strong, Kicked by a Moose Scotch Ale, Russian Imperial Stout, Sparkling Elderflower Wine, Barolo Wine, On Deck: Orange Pale Ale IV, Hidden Lake Nut Brown, 2H IPA III