Central-limit estimates of parameter standard errors are obtained from the diagonal terms of the inverse of the normal equations matrix. The covariance matrix is computed by multiplying each term of the inverse normal matrix by the weighted error-variance. It is used to estimate parameter error correlations and to compute confidence bands around the fitted curve. These show the uncertainty in the fitted curve arising from sampling errors in the estimated parameters, and do not include the effects of errors in the independent and dependent variables. The page also computes a generalized correlation coefficient, defined as the square root of the fraction of total y variance explainable by the fitted function.
Unequal weighting is accomplished by specifying the standard error associated with the y variable.
Standard errors can also be entered along with the x and y variables. If a transformation is applied to the y variable, the program will adjust the weights appropriately. The current implementation is limited to eight parameters and eight independent variables. These arbitrary limits could be increased without much trouble if necessary. I've used this page to fit 500-point datasets with no problems.