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 \degr 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 \degr from the rotation axis . Spectral fitting of the very strong field in TWA 8A ( in individual lines , simultaneously for Stokes I and V ) yielded a mean magnetic field strength of 6.0 \pm 0.5 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 \sim 4300 K , with hotter stars being less axisymmetric and poloidal , regardless of internal structure .