`Gamma()$aic` and `gaussian()$aic` seem inconsistent as the first increases linearly with the sum of the prior weights of the model, while the other doesn't.
Both of the behaviors seem justifiable (even though I'd prefer the second), but it seems desirable to be consistent, as many other functions (including `logLik()`) seem to rely on it as a proxy for the log likelihood of the model.
MIN REPEX, where we can see that the gaussian likelihood fails at being multiplied by two when the weights are doubled:
glms$g1 <- glm(data = USArrests, Assault ~ UrbanPop + Rape, weights = rep(1, nrow(USArrests)))
glms$g2 <- update(glms$g1, weights = rep(2, nrow(USArrests)))
glms$G1 <- update(glms$g1, family = Gamma("identity"))
glms$G2 <- update(glms$g2, family = Gamma("identity"))
sapply(glms, '[', "aic")