1. Literally, to continue moving, swinging, bending, tilting, etc., slowly in one direction and then back in the opposite direction. The structure swayed to and fro, threatening to topple at any given minute. Everyone in the crowd was swaying to and fro in time with the song.

2. By extension, to oscillate between two opposing positions, decisions, inclinations, points of view, etc. Public opinion has swayed to and fro on this issue for decades. You can't keep swaying to and fro over this—you need to make a decision and commit to it!