Normalize Weights in fitting a curve I am trying to fit a curve to set of data points. I have a set of weights that I want to assign each point while fitting. My question is that should i normalize the weights or use the weights as they are?
Are there any pros and cons of following one approach over the other.
Pardon me if the question is all too basic and it would really help if you can point me to some literature.
 A: Since you have not specified how your "weights" enter your particular model, it is not possible to definitively say what you can and can't do with them.  However, in most models that use weights, the model is amenable to any weighting vector that has non-negative weights.  It is usually possible to scale the weights to "normalise" them, but in most models this is not necessary.  Nevertheless, it can make sense to normalise a weighting vector to make it comparable to the standard case where there is no weighting.
In a standard statistical analysis, all the data points have the same weighting in the analysis, which means that they all have an implicit weight of one.  Thus, in a standard analysis with $n$ data points you could say that you have an implicit weighting vector $\mathbf{u} = (1, ..., 1)$.  Since there are $n$ values, we have $||\mathbf{u}|| = \sqrt{n}$.  Hence, if you want to normalise a weighting vector $\mathbf{w}$ to give the magnitude of the standard case you would usually set the normalised weight vector as:
$$\tilde{\mathbf{w}} \equiv \mathbf{w} \cdot \frac{\sqrt{n}}{||\mathbf{w}||} \quad \quad \quad \implies \quad \quad \quad ||\tilde{\mathbf{w}}|| = \sqrt{n}.$$
