First day I just put on two small split shots. The next day I bought a sinker designed for drop shot (like the one at the link below). In both cases the weight was 1/8 oz or less. I'm fishing in a pond, so there is no current. I only needed enough weight to get to the bottom but not so much that the sinker would get stuck in the crud on the bottom.

Voss Drop Shot Weights 6pk - Tackle Warehouse