Holding Obligations should add influence.
Currently the only way to gain influence is through declaring rivalries. Essentially, the only way to allow yourself more diplomatic actions is to make enemies. I like having this as a feature, but I also think there should be a way of expanding your influence capacity by doing things other countries actually like. Obligations are currently useful but I feel the influence and diplomacy side of the game could use some work, but I really would hate to see it become unnecessarily convoluted like so many parts of this game are.