Weight below the flies would probably keep them from tangling less, but your flies will be constanly pulled on a tight line even on a dead drift, so they are not being presented naturally.
The weight is to help get the flies in the right feeding lane, but you want to keep them drifting and moving naturally with the movement of the current once in that lane. Long tippet helps with this too, not to mention spooking the fish less. Long tippet will help them sink faster because their is more slack line than with a short line after a good and correct mend.
As a tip with tangling less droppers, open your loops up a bit and make sure your not making your foreward cast too soon.