w1' = w1 / w1+w2+w3 = 0.2/0.9 = .2222222...
w2' = w2 / w1+w2+w3 = 0.3/0.9 = .3333333...
w3' = w3 / w1+w2+w3 = 0.4/0.9 = .4444444...
w1'+w2'+w3' = 1.0
The weight fill-in for vertices with a weight less than 1 will always fill with the weight of the root. Whenever a vertex is assigned to a group of links, all of which are partially blended, then the remaining weight will be assigned and blended with the root link.
This works well for a case where you want partial deformation falling off to no deformation. An example would be a static head, where you are deforming the head for facial expressions, but the head itself remains in place.
The sum of these vertex weights is w1 + w2 + w3 = 0.9 (less than 1.0). We need an additional fill-in weight (wf). The fill-in weight is determined by 1.0 - (w1+w2+w3) = 0.1, or 10%. Physique fills in with weight wf from the root (leaving the vertex partially undeformed).
The vertex weight fill-in in overlap areas will be based on the percentage of partial and non partial weights. For example, If the total weight of non partial links is 80% of the total summed partial and non partial weight, then 80% of the fill-in will be more of the non partial deformation. The remaining 20% fill-in will come from the root.
Let's assume l1 and l2 are nonpartial, and l3 is partial. The nonpartial weight is w1 + w2 = 0.5; the partial weight is w3 = 0.4; the nonpartial weight is 0.5/(0.5+0.4) = .555555, or 56%; and the fill-in weight is still (1.0 - .9) or wf = 0.1.
Physique fills in with 56% of wf with more of the nonpartial blended links. The remaining 44% of wf is filled in with the root as in the partial blended case. This provides a smooth transition between the partial and nonpartial links.