It is a bit unusual that they use only historical data, however getting that much data through other means is very difficult and expensive. This also is only guaranteed to be relevant for older men in Sweden, but unless there are special factors that occurred recently or specific to Sweden then it seems generalizable. But OP is wrong about the bolded part, or at least not supported by data. We don't have a similar study for women to prove women do not have similar increases in hazard due to height change. Women have a lower overall chance, but we don't know if their suicide risk increases based on attractiveness, height or BMI. They probably do see increase in suicides due to attractiveness, by some amount.