Fitting weighted polynomial regression model

Hi,

I have a simple question but I just couldn't find the right way to do
it after 3 hours of hacking and google.

How do I fit a weighted polynomial regression model to my plot?

This is what I got so far:

lines(loess(A~B + I(B^2),weights=1/B^2))

Error in xy.coords(x, y) : 'x' and 'y' lengths differ
In addition: Warning messages:
1: pseudoinverse used at 0.52416 0.029047
2: neighborhood radius 3.8766
3: reciprocal condition number  4.3293e-017
4: There are other near singularities as well. 19.538

Any idea would be appreciated.

Thanks,
cruz