Bhaga is one of the clearest cases in the Rigveda of a god who is an abstract noun standing up. The word bhaga means a share, a portion, the part that falls to a person, and it is used constantly in ordinary contexts: the share of spoil, the share of an inheritance, the part of a sacrifice that belongs to a particular god. Bhaga the Aditya is that word addressed.
Because of that the hymns talk about him in a grammatically odd way. A worshipper asks to obtain bhaga, to be rich in bhaga, to have Bhaga on his side, and the same sentence can be read as a request for a good portion or as a request for the god's attention. The Vedic poets clearly enjoyed the ambiguity and worked it. One much quoted formula asks that the worshipper be a sharer in Bhaga, which is a pun in the original and an accurate statement of the theology.
He belongs with Aryaman and Amsha in the part of the Aditya group that deals with distribution rather than with law or oath. Where Varuna punishes and Mitra binds, Bhaga divides. He is also, in a few passages, said to be blind, and although the tradition offers stories to explain this, the plainer reading is that the apportioner does not look at who is receiving, which is the same intuition that later put a blindfold on the western figure of Justice.