I understand that SPSS supports only frequency weighting and I also understand how the output works.

However, I am confused on the part that how does weighing on frequency work? Is there a formula or what?

Say for example, I am running descriptive statistics before and after weighing.

I see that the frequencies before and after weighing are different. So how does that happen?

You can refer the document regarding the descriptive statistics here

In FREQUENCIES, the weight is treated as a replication weight. For example a case weight of 2 is equivalent to duplicating that case. With fractional weights, the behavior is procedure specific. Weights might be rounded or truncated or sometimes not used at all. CROSSTABS provides several options.

The CTABLES procedure can treat the weight as effective base weighting, which does not change first moment calculations such as the mean or count from replication weighting but adjusts second moment calculations such as standard deviation.

The Complex Samples procedures treat weights as inverse probability of selection and adjust accordingly. And, in a different usage, the TREES procedure can use an importance weight.

I understand that. But I still fail to understand how does descriptive statistics change due to the frequencies. How does frequency weighting work and affect the frequencies in Descriptive statistics to change?

The story is the same. In Descriptives, the weight is treated as a replication weight just as with Frequencies. Generally speaking, you should normalize the weights so that the sum of the weights equals the actual N in your data.

If you want to see the actual formulas, look up the procedure in the Algorithms documentation, which you can find here

ftp://public.dhe.ibm.com/software/analytics/spss/documentation/statistics/26.0/en/client/Manuals/IBM_SPSS_Statistics_Algorithms.pdf

Thanks a lot Jon! Really appreciate it