In fitting procedure, there is a opition to choose weights. I don't which type I should select. I read the build-in help of Origin but I don't find the information i wanted. can anybody do me a favor to explain what does weights mean? and which situation they are used?
I presume you are referring to the NLSF nonlinear curve fitting tool. With that tool active, go to the Options->Control page of the tool and press F1 key. In the help page that comes up, click the "The Weighting Method Drop-Down List" link. Then click the "weighting method" link in that help paragraph. This should open a topic called "Before you start: The Chi-Square minimization" which explains how weighting is used in the minimization process, and what types of weights are allowed.
Typically weighting is used when there are errors associated with the measurement, and you have for example an x, y, and yerr column that you are fitting to. But weight type can also be statistical in which case the weighting term is just 1/y etc. You need to decide what weighting method is suitable for your data.