i think regardless of whoever set it up, that petition makes a lot of sense as a matter to debate in parliament. If voter turnout isn't that high and the margin of victory isn't that great, then it seems pretty important for parliament to have a good deep discussion about what to do in terms of enacting the result of a referendum. Certainly the Leave vote won, but at the end of the day less than 40% of possible voters held that position.
The government absolutely has to give consideration to the will of the 17 million people who voted to Leave. But they also have a responsibility to the 16 million people who voted Remain and to the ~10 million people who for whatever reason didn't vote. This is a complicated situation which has already divided the country and could divide it more. If more time needs to be taken to ensure a majority of people really understand and want what they're getting then I think (within reason) that time should be taken.
There's certainly going to be a challenge to keep the EU happy so there can't be too many delays, but at the moment there isn't even all that much clarity on what a Leave vote is meant to mean. No ties with Europe at all? The same kind of relationship that Switzerland and Norway have? Some kind of split regulation that enables London to continue as the financial hub of Europe? The government has a lot of major decisions to make that will completely change to tone of what a Brexit actually means, and if you're going to have people vote on the idea of leaving in the first place they really should have the chance to digest what that will actually mean.