"ballooning mechanisms are not fully explained by current aerodynamic models. The global atmospheric electric circuit and the resulting atmospheric potential gradient (APG) provide an additional force that has been proposed to explain ballooning"
So perhaps a combination of drag and electrostatic force. And, unless the spider can build up a substantial charge on the thread, I am guessing that drag is the more important part.
The surface of spider thread is such that air blowing across it takes away charge, leaving behind the opposite charge.
So, atmospheric drag provides horizontal motion, and electrostatic repulsion provides vertical motion. Once the spider is aloft, air motion relative to it falls off, and the charge begins to leak away. Eventually it descends.
The rising convective air dragging along a vertical thread also provides some lift.
I wonder if anyone has tried to lift a spider using electrostatic forces alone and what voltage that would need? You'd think it wouldn't that hard an experiment to do.