The help for LSU states:
You pick a weight factor (the default value is 1) for the extra constraint equation. This weighted unit-sum constraint is then added to the system of simultaneous equations in the unmixing inversion process. Larger weights in relation to the variance of the data cause the unmixing to honor the unit-sum constraint more closely.
To strictly honor the constraint, the weight should be many times the spectral variance of the data. For example, If you use a weight of 100 with data that range from 0 to 1, it'll be a "heavy" weight and the fractions will be near unit sum. The same weight of 100 for data that range from 0 to10000, will be a very "light" weight, and this extra equation will have almost no effect. To get the same effect you'd need weight to be 1000000. It's the ratio that matters not the size of weight alone.
You might also consider why it may be misleading to use constraints:
http://www.harrisgeospati...leID/19704/1630.aspx