I read Willoughby's "I am very drunk .... enough to overset me" line differently. I think he is speaking ironically here, rather than claiming to be drunk.

Firstly, Elinor can see at once by "the steadiness of his manner and the intelligence of his eye" that he was sober. If he had been trying to convince her that he was drunk I don't think it would have been difficult for him to act as though intoxicated.

Also, Marlborough is about 40 miles from Cleveland - a good four hour drive. Porter was a dark, malted beer with a strength of about 7% at most. In a hard-drinking age a pint of porter was trivial. Willoughby might have felt slightly mellow when he left Marlborough but could not possibly have been drunk on his pint of porter by the time he reached Cleveland, and Elinor would have known that.