Despite extensive Monte Carlo (MC) simulations, the nature of the phase transition in the anisotropic planar rotor (APR) model remains elusive. The ground state is sixfold degenerate, which would naively suggest strongly first-order q=6 Potts behavior. Extensive MC simulations indicate either a second-order transition with q=3 Potts exponents, or a very weakly first-order transition. We show that the APR model maps to a generalized six-state Potts model, with a bond energy between pairs of Potts states q and (q+3) mod 6 larger by a factor alpha=alpha (APR)greater than or equal to2. For alpha=alpha (T)approximate to2.5, there exists a tricritical point separating first-order behavior (including q=6 Potts at alpha =1) from second-order behavior (including q=3 Potts at large alpha). Thus the APR model is weakly first order because of the proximity to this tricritical point.