The weight of a group is the minimal number of elements that normally generate the group. The (unsolved) Wiegold problem asks if there are finitely generated perfect groups with weight greater than one. It is conjectured that taking free products typically increases the weight, but there are limited tools for proving lower bounds of weights. I will explain how sharp lower bounds of a suitable complexity notion of surface maps (relative to the boundary) can be used to show some free products have weight greater than one. This relates the problem to the analogous spectral gap properties of stable commutator length (scl). I will sketch a method of Calegari proving spectral gaps of scl in hyperbolic manifold groups and explain how it can be adapted in the new setting.
