We consider a multi-access two-way relay network where multiple pairs of users exchange information with their pre-assigned partners with the assistance of an intermediate relay node. Each pair is assumed to have a shared channel which is orthogonal to the channels used by the remaining pairs. We investigate the relay power allocation problem for two-way relaying protocols that allow a variety of forwarding mechanisms, such as decode-and-superposition-forward (DSF), decode-and-XOR-forward (DXF), amplify-and-forward (AF) and compress-and-forward (CF). Different from one-way communications, in two-way relaying, the rates of the two communication directions between a pair of partners constrain each other, and the relay power allocated to one user pair simultaneously affects the rates of both directions. For each relaying scheme, we solve the problem of optimally allocating relay's power among the user pairs such that an arbitrary weighted sum rate of all users is maximized. Simulation results are presented to demonstrate performance of optimum relay power allocation, as well as the comparison among different two-way relaying schemes.