First thing -- DO NOT wash them. You will never get all the moisture off of them and inevitably you will have a steam explosion from the melting pot as you add weights --and a splattering of liquid lead on any part of your body is excrutiating, and potentially disastrous.
As the weights melt, steel clips, dirt, and all manner of detritus will float to the top. Skim it off. Once you've skimmed all you see, add a bit of paraffin (candle wax) as a flux and stir. Notice -- this will produce copious amounts of smoke and is best done outside, or at the least in a spot where there is strong, direct ventilation! Now you'll see more dirt and scum on the surface. Skim it off. Repeat the process. Depending on how dirty your weights are, it may take 4 or 5 cycles of fluxing, stirring, skimming. Once you've gottten all you're going to get, it is ready to pour up in to ingots.