If you listen closely when he gives it to Amy, she and Rory realise that the nanocloud doesn't effect Time Lords. Though why the Doctor didn't give his wristband to Amy as soon as he realised she'd lost hers is never explained, since Amy undergoes a degree of influence by the nanocloud whilst with the Doctor that could have been easily prevented.
- And it wasn't an "anti-gravity" wristband as stated in the question.