The effect is on the petitioners. By signing the petition it puts that issue more front and center in their minds. They will be more aware of this issue going f

The effect is on the petitioners. By signing the petition it puts that issue more front and center in their minds. They will be more aware of this issue going forward, for example when it comes time to vote or make a consumption decision. If you sign a petition against Nestle you are probably more likely to avoid their products in the future (causatively, i.e. the act of signing itself makes you less likely to buy Nestle, since you've put your name out there publicly against Nestle).