Hi,
you can simply impose a symmetry boundary condition for Stokes (or Navier-Stokes) flow as follows. The symmetry boundary condition states, that there must be no flux through the surface of symmetry and that the tangential component(s) are free. Therefore, the condition is given by
u \cdot n = 0
where n is the unit normal on the symmetry boundary.
As your symmetry boundary is given by the vertical line at x[0] = 0, the unit normal is given by n= [0,1]^T, so that the above condition is equivalent to u[0] = 0.
Therefore, in your code, you can impose this condition using
bcu_sym = DirichletBC(W.sub(0).sub(0), Constant(0.0), centre)
But the question that @Navier raised regarding your weak form, is of course still valid. Are you trying to impose a certain pressure level at the outlet?