The enhanced and broad Balmer lines evident in spectrophotometry of the white dwarfs PG 1658 + 441 and PG 0136 + 251 were previously interpreted in terms of comparatively weak surface magnetic fields, in the range 1-3 MG. New CCD spectrophotometry and circular spectropolarimetry confirm a magnetic field of mean surface strength B(s) = 2.3 +/- 0.2 MG on the former star, but provide only marginal evidence for a much weaker longitudinal component of B(e) = - 75 +/- 35 kG (1-sigma) on the latter object. Through detailed spectral modeling of the Balmer series profiles, it is now clear that the line enhancement in each star arises largely through the intensified damping on a very high gravity object: for PG 0136 + 251, log g = 9.00 +/- 0.10, indicating a mass of 1.20 +/- 0.04 M.; for PG 1658 + 441, log g = 9.36 +/- 0.07 and M = 1.31 +/- 0.02 M. (error bars represent formal fitting uncertainties). Indeed, PG 1658+441 is the highest mass single white dwarf reported thus far. Assuming normal stellar evolution, these values and the stars' high temperatures (T(eff) = 39,190 +/- 360 K and 30,510 +/- 200 K, respectively) imply extreme youth, both on and off the main sequence. However, their locations, at high Galactic latitude and well away from any clusters of similarly young stars, are perhaps more consistent with origins in recent stellar mergers. A mass near the Chandrasekhar limit for PG 1658+441 adds evidence for a relationship between surface magnetism and mass among white dwarfs in the field.