Sentence:  He had his tea and hot rolls in a morning, while we were battening upon our quarter-of-a-penny loaf — our "crug" — moistened with <WSD>attenuated</WSD> small beer, in wooden piggings, smacking of the pitched leathern jack it was poured from. 
Meaning of the word marked with <WSD> tags:  Made, or become weak; subject to attenuation.