There was actually a meta-petition[1] recently that was asking for the White House to pay more attention to these petitions, so it seems like these petitions are mostly ignored
[1] https://wwws.whitehouse.gov/petitions/%21/petition/actually-...
[1] https://wwws.whitehouse.gov/petitions/%21/petition/actually-...
The petitions are not there for us to influence them. They're there (they spent effort to put them there) for them to influence us.