1) I would think that Armadillos or Gatoerskins are better than stop-flat and yes weight sure does matter!!
2) When my tires get cut up I replace them. The cost of tires is relatively low and a new set once or twice a year is not a big deal. Most of us spend thousands on the bike why cheap out on tires?
3) Like most of us on BF I have found the Conti 4000-S is the best compromise with regard to flat protection, wear, performance and weight.