Here we present new adaptive optics observations of the Quaoar-Weywot system. With these new observations we determine an improved system orbit. Due to a 0.39 day alias that exists in available observations, four possible orbital solutions are available with periods of ̃11.6, ̃12.0, ̃12.4, and ̃12.8 days. From the possible orbital solutions, system masses of 1.3-1.5 ± 0.1 × 1021 kg are found. These observations provide an updated density for Quaoar of 2.7-5.0 g cm-3. In all cases, Weywot's orbit is eccentric, with possible values ̃0.13-0.16. We present a reanalysis of the tidal orbital evolution of the Quaoar-Weywot system. We have found that Weywot has probably evolved to a state of synchronous rotation, and has likely preserved its initial inclination over the age of the Solar System. We find that for plausible values of the effective tidal dissipation factor tides produce a very slow evolution of Weywot's eccentricity and semi-major axis. Accordingly, it appears that Weywot's eccentricity likely did not tidally evolve to its current value from an initially circular orbit. Rather, it seems that some other mechanism has raised its eccentricity post-formation, or Weywot formed with a non-negligible eccentricity.