Weight command sets a weight for a vertex or a line to make a non-round object by applying a patch (subdivision surface).
A method for setting weights are different by a type of a patch. When you active the Weight command, a type of a patch applied to the current is set as the [Target], and it is not necessary to change the target usually.
Weight is only available for [Spline type 1] or [Spline type 2] patches. Weight can be set from -1.00 to 1.00. A shape is modified in real-time when you 
drag a vertex or a line.
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| Weight = 0.00 | Weight = 1.00 |
A weight is not applied for a Catmull-Clark patch.
A crease for an edge is available for a Catmull-Clark patch. After clicking an edge, a crease of the edge will be switched, and creased edges are highlighted. The following image is an example for applying creases to the edge on the top face.
Creases can be also set by [Menu > Attribute > Edge crease for Catmull-Clark].
A weight for a vertex or a line is set for OpenSubdiv. A range of weight is from 0 to 10. A shape is modified in real-time when you drag a vertex, a line or a face.
A vertex or a line applied weight is highlighted. Weights are applied for 4 points in the top face in the following picture.
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| Vertex weights = 10.00 | Vertex and line weights = 10.00 |