  We present a spectropolarimetric study of two weak-line T Tauri stars
(wTTSs), TWA 6 and TWA 8A, as part of the MaTYSSE (Magnetic Topologies of Young
Stars and the Survival of close-in giant Exoplanets) program. Both stars
display significant Zeeman signatures that we have modelled using Zeeman
Doppler Imaging (ZDI). The magnetic field of TWA 6 is split equally between
poloidal and toroidal components, with the largest fraction of energy in
higher-order modes, with a total unsigned flux of 840 G, and a poloidal
component tilted $35^{\circ}$ from the rotation axis. TWA 8A has a 70 per cent
poloidal field, with most of the energy in higher-order modes, with an unsigned
flux of 1.4 kG (with a magnetic filling factor of 0.2), and a poloidal field
tilted $20^{\circ}$ from the rotation axis. Spectral fitting of the very strong
field in \tb (in individual lines, simultaneously for Stokes $I$ and $V$)
yielded a mean magnetic field strength of $6.0\pm0.5$ kG. The higher field
strengths recovered from spectral fitting suggests that a significant
proportion of magnetic energy lies in small-scale fields that are unresolved by
ZDI. So far, wTTSs in MaTYSSE appear to show that the poloidal-field
axisymmetry correlates with the magnetic field strength. Moreover, it appears
that classical T Tauri stars (cTTSs) and wTTSs are mostly poloidal and
axisymmetric when mostly convective and cooler than $\sim4300$ K, with hotter
stars being less axisymmetric and poloidal, regardless of internal structure.
