Adding weight above lure of any weight at any distance will alter its action. Even large/heavy swivels can tighten or reduce action (line to line knots are more useful).
However if you're using something like an inline spinner or spoon, where there isn't much/any erratic action, you can use weights and swivels (for spinners definitely use swivels). Just keep them at least 3 feet above the lure, so fish don't get too suspicious.
So its all about the type of lure, but if you are having trouble in current, it also depends on where you cast, how quickly you pick up the slack, and how you have positioned yourself along the bank. Fishing on the point of the inside of a bend, you get good swing distance. The opposite is true for when fishing the outside of the bend. If fishing deep water and fast current, cast at a further angle from the middle upstream, and don't pick up the slack right away (keep rod tip up). If the current is fast enough, within seconds your line will already be tight (now slowly bring your tip down to add quick depth), and now to get deeper you can just inch the line through your fingers.