better and best as forms of adjective and adverb
Better and best (and worse and worst) are suppletive in many languages: Latin bonus ("good"), melior ("better"), optimus ("best"); Russian добрый (dobry, "good") лучше (lučše, "better"); Welsh da ("good), gwell ("better").
As for better and best serving for both adjective and adverb: I suspect it is well which is suppletive, replacing any derivative of good.