The word weight has many uses in mathematics. It can refer to a function 
(also called a weighting
function or weighting function) used to
normalize orthogonal functions. It can also
be used to indicate one of a set of a multiplicative constants placed in front of
terms in a moving average, Newton-Cotes
formulas, edge or vertex of a graph or tree,
etc. It also refers to the power 
in the multiplicative factor 
defining a modular form.
The weight of a tree at a point 
is the maximum number of edges in any branch
at 
(Harary 1994, p. 35).
