Skinning a rig to a mesh is the process of binding the skeleton under the mesh or skin to actually influence and control the mesh's position, effectively animating the mesh. this is a fairly simple process and requires that one simply select the join hierarchy the mesh together and conduct a smooth bind operation which also applies a set of basic skin weights.
Painting weights, as it turns out, is one of the most pain staking and frustrating processes I have yet to encounter in 3D modelling and pips UVing at the post in this regard. The reason for my disdain is the fact that the entire process feels so imprecise and each action taken to correct one issue then creates more issues elsewhere. Its an unfortunate case of one step forward, two steps back. Skin weighting is essentially granting influence to certain certain joints over vertices on the mesh. It is similar in a sense to blend shapes except that it is far more complicated. In essence each joint must have total control over its own area of the mesh as well as a smooth decrease in influence away from the area as to not create sheer drop off points that look unnatural and ugly, on the other hand having too much of a smooth gradient will result in either insufficient influence over certain areas or over influence in areas which it has no business influencing. It is a delicate balance and something that is never truly finished, only that you get to a point where it works well enough for your purposes.
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