In "Gnomes", the store was in danger of going out of business when rival Harbucks coffee came to town. It remained in business, despite the coffee's "rancid sewage" flavor. At the end of the episode, the Tweak family and Harbucks form a business deal to allow the shop to remain open.
The building was seen again, with a new appearance mimicking the Starbucks coffee chain, in the episode "201", where it was nearly destroyed by Mecha-Streisand until the Super Best Friends intervened.
Tweek Bros. Coffee appears prominently in the game, with the design from "201". It serves as one of the shops where the player can purchase 'potions', including special blends of coffee, and is featured in a couple of quests which require the player to pick up coffee deliveries and other items. It is shown that only the Tweak family works inside the building, which has a large interior. It is located between the Bijou Cinema and U-STOR-IT.
Tweek seems oblivious of why he's so addicted to coffee, at most thinking of the delivery as some kind of special ingredient.