As well as agreeing with most of what Gardener says(whats new) I think that a weighted fly works well on small rivers with pools that have a heavy flow and deepn short pools. The Findhorn gorge section springs to mind. The fish lie in the heavy water waiting to shoot the falls to the next pool, with a light fly even on a sinking line/tip the fly doesn't get down to the fish. My secret weapon was a yellow Ali Shrimp (the water was the colour of a fine malt) with a lead film below the dressing. Magic.
On larger rivers Ness Spey etc I prefer a unweighted Waddinton even when the water is just above freezing. I use a fast sink tip in these conditions