Why do you think the results are wrong? I just ran your program with plots turned on, and everything looks fine for the fit. Taking out the weight statement gives a different confidence region, different SE, etc.,as expected. I think you just have a coincidence about the "0.1". For instance, I ran:
data b; set startdata; pred = x**2; SS = (y - pred)**2; WSS = z*SS; run; proc means data=b sum; var SS WSS; run;
To manually get the sum of squares, weighted and unweighted, based on your parameter estimate. Weighted SS = 0.1, just like the NLIN output. If you run NLIN without the weight, you get SS = 1.0. This is what you get manually (above). I think everything is fine. By the way, put a plots=all option in your NLIN statement for good graphs.
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