He prefers to serve only the upper class, noting that he is only trading with the Sole Survivor "because he is programmed to oblige." He sells flamer fuel, food and drinks.
Wellingham and Piper Wright have a unique dialogue together that reveals that Wellingham is secretly an informer for her, dishing out gossip about the city's upper class members. His apparent scorn towards the city's lower classes seems to be just a cover to avoid suspicion, at least in regards to Piper.
If Nick Valentine is taken up to the Colonial Taphouse balcony there's a chance for a conversation to trigger where Wellingham asks if Nick has "reconsidered" his offer to become his new detective partner. Nick doesn't sound very intrigued by the idea.