Let's say you have your function:
Now, you have your data set and weights:
I'll assume that W is positive, where higher values have more influence...
So, you want an objective function that accounts for these weights:
wobj = @(p,x,y,w) = sum(w .* (f(x,p(1),p(2)) - y) .^ 2);
Here I've calculated the square difference between your function f and the data y, multiplied that by the weights, and then summed the result. That might not be the correct way, but bear with me - I'm not a mathematician!
Finally, you wrap it all together. Since I'm used to fminsearch I'll use that, but there are probably better functions available that will minimize on an objective function.
p0 = [a0, b0];
p = fminsearch( @(p) wobj(p,X,Y,W), p0 );
a = p(1);
b = p(2);
If this isn't quite right, it ought to be close =) Perhaps I should've divided those weights? Erkk, brain doesn't want to think about it right now.