You get drunk off just one centimeter?! And Kensuke was supposed to be a heavy drinker.
Literal
Just 1-centimeter [with-で] get-drunk [polite-ますか]! Kensuke [topic-は] heavy-drinker [copula-だった] [quot-と] say [even-though-のに].
たった 'mere / only' is the emphatic intensifier for small quantities, stronger than plain 一. で here is the causal/instrumental 'with / by means of / thanks to.' ~と言うのに is the concessive 'even though they said X.' 酒豪 '(a) heavy drinker / a drinking champion' is a respectful / admiring compound for someone who holds their liquor well, formed from 酒 + 豪 'mighty one.'