We report $^{51}$V NMR, $mu$SR and zero applied field $^{63,65}$Cu NMR measurements on powder samples of Sr-vesignieite, SrCu$_3$V$_2$O$_8$(OH)$_2$, a $S = 1/2$ nearly-kagome Heisenberg antiferromagnet. Our results demonstrate that the ground state is a $mathbf{q} = 0$ magnetic structure with spins canting either in or out of the kagome plane, giving rise to weak ferromagnetism. We determine the size of ordered moments and the angle of canting for different possible $mathbf{q} = 0$ structures and orbital scenarios, thereby providing insight into the role of the Dzyaloshinskii-Moriya (DM) interaction in this material.
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