Your question almost makes me want to add fishing distances expected as another criteria for selecting certain line weights. This being besides fly size.
At the S/E FFF Conclave several years ago Rick Pope from TFO had a light rig set up for the hot shots to see how far they could cast it. Really, it wasn't pretty making a rod do what it really isn't designed for. I'll say the same about your question. For a short 1-2-3 weight I would expect to comfortably cast them 5-50'. You might get more distance with effort and good technique but distance isn't why one usually gets rods like that.
A 4 weight and beyond will definately expand your fishing range but then you'll probably lose some of the fun factor of catching on a light weight rig.
Whatever you decide, have a blast with it!