Okay, so maybe "heavyweight" is too strong of a term, but there's several ways to add weight to your fly during the tying process to help it sink faster. While of course every fly isn't weighted, having some heavier patterns on hand can make a huge difference in your success. Let's run through a few ways to easily add extra heft to your bugs!
Weighted Heads: Adding a weighted head to your fly can be as simple as sliding it onto the hook and up against the hook eye. Weighted heads may come in the shape of a round bead, cone, fish head, or other varieties. Since they are usually made of something like brass or tungsten, the head will help your fly sink into the strike zone just a bit quicker and can even add a hint of fish-attracting flash. Think of it sort of like a tiny jig head!
Bead Chain/Dumbbell Eyes: Specialty eyes are another great option for adding weight to a fly. Bead Chain eyes are sold as one long chain-like piece and must be cut from the length with cutters. Dumbbell-style eyes are sold individually and are ready to tie-on right out of the package. They may also come painted/detailed which adds a nice touch of color and realism. Eyes can be made from materials such as brass, lead, and tungsten.
Wire/Thread: One of the most versatile ways to weight a fly is by using wire. Often made with lead, there's also non-lead versions available. Using whatever amount is desired, the wire is commonly wrapped around the hook shank before the body of the fly is constructed. Other types of colored wire may also be used to construct the actual body of a small fly or as "ribbing" that's widely wrapped over material. Tungsten thread is another option for those seeking to add weight to very small flies since it comes in fine diameters.