Both functions have the same purpose, so theoretically there is no need to have both.

But they have some differences:

resolve_tri_uv_v2:
Advantages:

• Much more precise because it works with double precision.
• The name is consistent with the existing ones: resolve_tri_uv_v3, resolve_quad_uv_v2, resolve_quad_uv_v2_deriv, resolve_quad_u_v2.

Differences:

• Returns a vector with 2 dimensions (uv[2]).
• If the triangle has zero area the returned vector is {0.0f, 0.0f}.

barycentric_weights_v2:
Advantages:

• Intensively used throughout the code.
• 30% more efficient.

Differences:

• Returns a vector with 3 dimensions (w[3]).
• If the triangle has zero area the returned vector is {0.333f, 0.333f, 0.333f}.

Proposed change:

• make barycentric_weights_v2 work with double precision (even losing performance).
• Replace 'resolve_tri_uv_v2' with it.

(The multires bake code has been tested with the patch).