I think the weakest corp id is obviously Custom Biotics.
Identity: Division • Deck: 45 • Influence: 22
You cannot include Jinteki cards in this deck.
First of all, I think HB is the faction that least needs to use influence. An increase in 7 influence is good, but not that significant. Unlike most other IDs, this one has a drawback and a relatively serious one. Not only are you preventing from using almost a quarter of the card pool, the runner knows which cards are not in your deck. Ice is a lot less scary when you don’t have to worry about scary Jinteki ice like Chiyashi, Swordsman, and DNA Tracker.
In theory, Custom Biotics is a good ID for a combo deck using high-influence, non-Jinteki cards, but several factors cause this not to work out in practice. First, not being able to use Jinteki cards essentially rules out net damage combos. Brain damage combos don’t really need the extra influence, especially since you can’t use cards like Neural EMP to finish the runner off. Meat damage initially seems like a good option because of the high-influence Weyland cards, but it often requires infrastructure to tag the runner from NBN. There aren’t any particularly synergistic HB agendas or high-influence cards for this strategy, so there’s not much reason to simply run a Weyland deck with NBN cards or vice versa. In addition, other HB IDs are significantly better for combo decks. Cerebral Imaging and Sportsmetal both have powerful abilities well-suited for combo decks and a full 15 influence.
tl;dr: The minor upside of Custom Biotics is counteracted by the minor downside, basically leaving us with a blank 45/15 HB ID.