1/2 N2 + 1/2 O2 = NO
ΔHo = + 21,590 g cal/mol
1/2 N2 + O2 = NO2
ΔHo = + 7,730 g cal/mol
So you are right in that the products of N2 and O2 are more stable than NO and O2.
the breaking of the second N-O bond requires quite a bit of activation energy though, which in turn requires a good catalyst to pull it off. Studies are conducted in what ideal catalysts for this reaction are