Old English bettra, earlier betera "of superior quality or excellence," from Proto-Germanic *batizo-, perhaps from PIE *bhad- "good," but Boutkan finds no good IE etymology. For etymology and evolution, see best. Cognate words also have become the comparative adjective of good in the older Germanic languages (Old Frisian betera, Old Saxon betiro, Old Norse betr, Danish bedre, Old High German bezziro, German besser, Gothic batiza). All are comparatives of a positive (Proto-Germanic *bat) which is not in use.
In Middle English the adverbial form commonly was bet, sometimes also was an adjective; bet was displaced by c. 1600. From late Old English as "improved in health, more healthy" (adv.); from late 12c. as "more useful or desirable." Better half "wife" is first attested 1570s.