the one problem with this petitions website, at least historically speaking, is that its been used purely as a political optics tool.
the only "requirement" if a petition garners enough signatures is for the administration to issue a response. there is no other action required. a "thank you for your petition and taking the time to sign" can be the offical response.
the obama administration used this to drive their agenda in the following way - if they got a petition that followed a wacky left wing view they had a document to wave around and issue a response saying "the people have spoken, look! thank you for your support". If they got a petition for a view that didn't fit the agenda, they'd issue a response similar to "thank you for your petition, this is why we feel your view is wrong, and why you're deplorable" and the spout a bunch of anti (issue) rhetoric.
however besides triggering a response these petitions have no teeth to them, or haven't anyway. Its not like they trigger an automatic proposal for legislative or regulatory action.
it will be interesting to see if the new trump admin continues to utilize the website as it has been, or if it actually generates some action other than a response to receiving the petition.