That is how raw weights work! You may wish to try standardized weights.

Edited and considerably expanded 12th July 2016 .

If you use unstandardized weights you are effectively increasing the number of observations as  the absolute numerical value is applied to the model - if 啊 weight at level 1 is 10 then you effectively have 10 people with the same response and predictors values. This is like you had observed the full population and using N instead of n will potentially have a great effect on  SEs,  variances , and CIs which use size in their calculation

 The standardized weights  stored in c1500 will in contrast have an overall mean of 1 so that you have not 'increased' the overall numbers just weighted them differently - the sample size is still the same.

If you have a multilevel structure the standardised weights are calculated so that the mean weight for each level 2 unit j is 1

A few more things

http://www.bristol.ac.uk/cmm/software/support/support-faqs/weights.html

More generally this paper  considers  " analyses that do and do not employ weights and design effects to illuminate the differential results of key parameters and standard errors using varying degrees of using or not using the weighting and design effect continuum (no weights, raw weights, relative or normalized weights, and design effect adjusted weights)"

"estimates derived from the application of raw weights to the data will be done based on the population size, N, rather than on the actual sample size, n (Kaplan & Ferguson,1999). Any estimates that are sensitive to sample size (e.g., standard errors,test statistics), therefore, will be affected when using the raw weight (Kaplan & Ferguson). Statistical packages such as SPSS treat the sum of the weightsas the actual sample size. Thus, if the raw weight is used, tests of inference most likely will be significant because the software is interpreting the population rather than the sample size"

"Normalized weights sum to the actual sample size, n (Kaplan & Ferguson; Pfeffermann, Skinner, Holmes, Goldstein,& Rasbash, 1998). Normalized weights address sample size sensitivity issues while still incorporating sample weights (Kaplan & Ferguson). Applying the normalized weight in the analyses ensures that the standard error estimates are correct given a simple random sample (Thomas & Heck)."

https://education.ufl.edu/educational-research/files/2011/01/Hahs-Vaughn_2005_Using-weights-with-national-datasets.pdf

Dear professor Jones,

Thank you very much. I will try it. I was puzzled about it because I have used weights before and did not have such a problem. 

But I will try standardized weights and see how it goes, it will probably reduce the variance.

Thank you very much for your help!