When the petcock is from an old Sachs moped, you may need to open it up to remove gunk and varnish. Simply screw the side off and view the inside to clean.
A few comments:
Not all moped petcocks are designed like the one pictured, but almost all are similar. This is one of the most common on older mopeds with 12mm x 1mm threads. It's also one of the most durable, with a metal handle. There are some integral parts of the petcock not shown in the picture:
1. One is a ~1/2" round, flexible gasket thing (nylon/neoprene maybe), with 2 or more small holes through it, like a button, that fits down into that cavity in the body of the petcock (on the right). It functions as the seal between the moving face of the handle parts (on the left), and the non-moving face in the cavity. When the petcock leaks, this gasket is usually the part that fails - due to wear. Unscrew the handle part from the body part to inspect/remove the gasket. If yours is intact, take care not to damage it (especially the edges). Re-install it with the flat face out, toward you in the picture. Whether your gasket has 2 or 4 holes, position its cleanest, roundest, 2 holes over the 2 holes in the cavity that the main tank and the reserve tank flow through, in this case, the bottom hole and the left hole. Cover the "off" hole, on the right here, with a solid part of the gasket to stop it from flowing. If after reassembly your gasket doesn't make a good seal, you need a new gasket. I recently saw them on offer for pennies at one moped parts webstore in Europe. In the US, I've never seen them. Or you'll need a replacement petcock (good luck finding an aftermarket one that lasts), OR you could make your own gasket, see http://www.youtube.com/watch?v=5DqvB_5gP20. To better understand what you're doing here, watch this video.
2. The hex-shaped section that appears in the picture to be one piece with the body of the petcock, is actually a separate part, i.e., a threaded sleeve. Most petcocks have these sleeves. It unscrews from the male threaded nipple under the fuel tank above it, and also unscrews from the threaded nipple of the petcock below it. Carefully unscrew both ends of the sleeve and remove it for cleaning. Inside the sleeve is a non-metallic washer (not shown). Don't lose it, and remember to reinstall it.
3. Most petcock bodies also have a 1" to 5" long, 1/4" round, fine-mesh, metal or plastic tube, the primary fuel filter, extending through and out of the sleeve. This filter is usually one piece with the petcock. Be careful with it in dis-assembly, cleaning, reassembly.
Finally, note the little tit on the black washer on the petcock handle. During reassembly, fit the tit in the slot at the bottom of the body of the petcock to line it up properly inside, then screw on the handle.