Many things, my friend. The list is simply too long. They usually end up using Scripture, Tradition, and reason. Tradition being from the Early Church Fathers not the Latin mass type of tradition. In my experience, they love using magisterial documents of the church to make it look like one Catholic doctrine contradicts another.
As for the 1979 BCP, it is pretty stupid, even Anglicans think this. Most Anglicans use the 1928 because it is more traditional and not influenced by recent problems like gays and woman ordination. 1979 BCP is not used by any other diocese of the Episcopal Church (TEC for short) which tells you something already. Plus TEC is suspended from meeting with all of the other Bishops in the Anglican communion because of heresies like woman ordination, gay marriage, etc.
Ok back to your other question concerning the 1979 copy Book of Common Prayer. Anglicans are basically Catholic in spirituality. Just without the Pope and some other theological issues. They have no problem admitting that they are Catholic because they think they are. But they are also protestant. Anglicanism is defined as the middle ground between Catholicism and protestantism because they are a mix of both, a lot of people find this appealing.
I like the 1928 BCP because it has beautiful prayers and prayers for all sorts of things, but I would only trust a 1979 bcp as a last resort.