  Topological Weyl semimetals (WSMs) have been predicted to be excellent
candidates for detecting Berry curvature dipole (BCD) and the related
non-linear effects in electronics and optics due to the large Berry curvature
concentrated around the Weyl nodes. And yet, linearized models of isolated
tilted Weyl cones only realize a diagonal non-zero BCD tensor which sum to zero
in the model of WSM with multiple Weyl nodes in the presence of mirror
symmetry. On the other hand, recent \textit{ab initio} work has found that
realistic WSMs like TaAs-type or MoTe$_2$-type compounds, which have mirror
symmetry, indeed show an off-diagonal BCD tensor with an enhanced magnitude for
its non-zero components. So far, there is a lack of theoretical work addressing
this contradiction for 3D WSMs. In this paper, we systematically study the BCD
in 3D WSMs using lattice Weyl Hamiltonians, which go beyond the linearized
models. We find that the non-zero BCD and its related important features for
these WSMs do not rely on the contribution from the Weyl nodes. Instead, they
are dependent on the part of the Fermi surface that lies \textit{between} the
Weyl nodes, in the region of the reciprocal space where neighboring Weyl cones
overlap. For large enough chemical potential such Fermi surfaces are present in
the lattice Weyl Hamiltonians as well as in the realistic WSMs. We also show
that, a lattice Weyl Hamitonian with a non-zero chiral chemical potential for
the Weyl cones can also support dips or peaks in the off-diagonal components of
the BCD tensor near the Weyl nodes themselves, consistent with recent
\textit{ab initio} work.
