I think you mixed up parameter estimator and weight of obs . It depends on how much important for a special obs in model and what do you want. by default , very obs has weight 1, if you think some one of obs is very important for the model, you can increase its weight, vice verse.
Did you check Rick's blog ? weight would not change other statistical like DF, STD ERROR . therefore it would not change parameter estimator.
As Rick's blog showed, if you want robust parameter estimator(there are some outliers in model) ,you should use weight of obs.
otherwise unweight.
Maybe you should ask Rick , who might give you more information.
P.S. I would choose 0.00128 ± 0.00011 (CI) , since STD ERROR is smaller than another.
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