Kammtail,
To make it short, if the float level is correct and the car runs OK once you get it going, then the problem is in the idle circuit. I would blow out all of the idle jets first. If it still does it, go one size larger on idle jet.
Basically all Weber carburetors have four circuits.
1. Idle
2. Cross-over
3. Accelerator Pump
4. High Speed running.
The Idle and Cross-over circuits BOTH draw their fuel from the idle circuit well. At idle all will be well. Once you open the throttles slightly, you will uncover the cross-over port(s) which are small drillings in the walll fo the throttle bore (covered by the throttle plate when it is closed). As you open the throttle intake manifold vacuum will draw fuel out of those drillings to provide additional fuel. This fuel comes from the "idle circuit fuel well". If the idle jet is too small, then not enough fuel will be available and the engine goes lean and "bogs". It may even stall. Increasing the idle jet should sizesolve this problem.
Paul
Scuderia Topolino