Hanger and Anchor Holding Power
Picture hangers with long nails that you pound into drywall at an angle are more robust than they appear and can support more than the 25 pounds for which they are rated. You won't get the maximum holding power unless you can pound the nail into a stud, though, and even then, you shouldn't use any hanger to support more than the weight for which it is rated. Toggle bolts are the strongest hangers for use in between studs -- they are recommended for weights up to 50 pounds -- and there are many in-between options. The best way to hang a picture heavier than 50 pounds is to suspend a plywood strip between a pair of studs.
The Plywood Strip Approach
Unless you live in an older house with plaster and lath walls, the most secure way to hang a picture is to drive a 3-inch screw into a stud, but finding a stud in the exact location you need it is a little like winning the lottery. If you screw a strip of 1/2-inch plywood to the stud closest to the planned center of the picture and adjacent stud, though, you can hang the picture from the plywood. It can hold the screws and heavy-duty picture hangers that drywall can't. For extra support -- and to prevent the picture from tilting -- it's better to attach two hangers to the plywood.
Make Your Own Braided Wire
Before you install the plywood on the wall, you need to make sure that the picture has a secure means of support. If you don't have any braided picture wire, you can make your own by twisting together strands of utility wire. An easy way to do this is to insert one end of several strands of wire into a drill chuck and clamp the other end to a bench with a clamp. Run the drill to braid the wires together. When you're done, stretch the wire between the two heavy-duty hooks you've screwed into the picture frame and secure the ends by twisting the wire. The wire should have enough tension to prevent it from clearing the top of the frame.
Hanging the Picture
To determine the distance of the hooks from the top of the painting, center a 6-inch piece of 1-by-2 lumber behind the picture, place it under the wire and support the picture on it. The distance of the top of the board from the top of the painting is the same distance that the hooks should be from the mark on the wall. Make a new mark to denote the centerline of the plywood strip. The 2- or 3-inch wide strip should be long enough to extend an inch beyond each stud. Pre-drill before screwing with a 1/4-inch drill bit; use a torpedo level to level the plywood strip; then secure it with 3-inch screws. Use the 1-by-2 to space the hangers; screw them into the plywood, and hang the picture.