  We present J-band imaging and H+K-band low-resolution spectroscopy of
2MASS1207-3932 AB, obtained with VLT NACO. For the putative planetary mass
secondary, we find J = 20.0+/-0.2 mag. The HK spectra of both components imply
low gravity, and a dusty atmosphere for the secondary. Comparisons to synthetic
spectra yield Teff_A ~ 2550+/-150K, and Teff_B ~ 1600+/-100K, consistent with
their late-M and mid-to-late L types. For these Teff, and an age of 5-10 Myrs,
evolutionary models imply M_A ~ 24+/-6 M_Jup and M_B ~ 8+/-2 M_Jup. Independent
comparisons of these models to the observed colors, spanning ~I to L', also
yield the same masses and temperatures. Our primary mass agrees with other
recent analyses; however, our secondary mass, while still in the planetary
regime, is 2-3 times larger than claimed previously. This discrepancy can be
traced to the luminosities: while the absolute photometry and Mbol of the
primary agree with theoretical predictions, the secondary is ~ 2.5+/-0.5 mag
fainter than expected in all bands from I to L' and in Mbol. This accounts for
the much lower secondary mass (and temperature) derived earlier. We argue that
this effect is highly unlikely to result from a variety of model-related
problems, and is instead real. This conclusion is bolstered by the absence of
any luminosity problems in either the primary, or in AB Pic B which we also
analyse. We therefore suggest grey extinction in 2M1207B, due to occlusion by
an edge-on circum-secondary disk. This is consistent with the observed
properties of edge-on disks around T Tauri stars, and with the known presence
of a high-inclination evolved disk around the primary. Finally, the system's
implied mass ratio of ~0.3 suggests a binary-like formation scenario.
(abridged)
