Not the OP but I’ve had situations of waiting at a weight-sensor-triggered left turn light for so long that I had to back up and turn right then u-turn.
FYI, they're usually not weight sensors, but instead they are triggered by a current momentarily induced by a large hunk of steel moving over top of them. If you find yourself in this situation in the future, you can try reversing and pulling up in a slightly different lane position. (preferably by braking harder, so as to increase your velocity over the sensor and the magnitude of the current induced.) Look for hexagonal cutouts in the asphalt and attempt to drive directly over them.