Drifting tonearm/cartridge weight

Have you checked anti-skate?

This is completely normal, the anti-skate applies a force in the direction of the outside of the record. If there is not enough friction between the bottom of the arm and the surface of the arm rest, the arm will float outwards. The answer is to increase the friction between the arm and arm rest. The Regas can have this problem. Make sure that the bottom of the arm and that little rubber bead on the top of the arm rest are very clean. Gently sanding the bead with very fine grit paper or steel wool may also help.

Viridian nailed it.

It's worth adding that you may have AS set too high, which would increase any outward drift while cueing. It's very unlikely you need AS set as high as your tracking force. If you have, try reducing it to half that amount or even less. You only need enough AS to track dynamic passages cleanly on both channels. Any more will cause sonic degradation as well as mechanical issues like these.