I've read the petition. Not one figure on there to even start off a business case. Exactly who is supposed to put the money up for this?
I can think of only two 'city' airports in Europe that seem to have some commercial success:
1. London (capital city, specifically serves one of the world's most important financial centres)
2. Florence (major international tourist destination).
With respect, Sheffield is neither of these, and both have significantly longer runways than SZD.
I wouldn't contemplate a 'city' airport in any British region. No economic case, especially given the multitude of full size airports.