Hi Emmy,
I think you are referring to Calibrachoa 'Million Bells' akd million bells.* Flowering is reduced in shade. The really prefer full sun.* Yours may also be rootbound and need a larger pot.* I've never had to deadhead them. You might want to move them to full sun and fertilize every two weeks with a balanced fertilizer or add timed release fertilizer when you repot. You might find this helpful.
http://www.mobot.org/gardeninghelp/p....asp?code=A119
http://msucares.com/news/print/sgnews/sg00/sg000207.htm
Newt
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.