If it were me, and I had ANY doubt whatsoever about whether my pet could lift the tiles at all, I wouldn't use them, or I would grout them. I would be so upset if my pet was injured by tiles I put in there.
I'm pretty sure they're heavy enough. Even if they somehow are not, since I will be.pressing them together as close as possible (even without grout) there shouldn't be any way to flip them over... if I'm making sense? I don't know if I'm explaining very well.