Not sure how to use "Weight" in "Analyze"

[#1]

I want to do something really simple. For simplicity's sake, assume I have two groups, let's say with N=2,000 in group 1 and N=3,000 in group 2. I'd like to compute an overall mean of a variable Y that is collected for each group. Y's mean in group 1 is 4 and in group 2 is 8. The overall mean here would be the unweighted mean and not the weighted mean–it should be 6. I might have thought that I should put in the following values for "Weight":

Group 1: 5,000/2,000

Group 2: 5,000/3,000

But those don't yield the expected number. Can you help me understand the "Weight" option in Analyze:JMP and tell me what weights I need to use for my problem?

[#2]

same example as above, with Graph Builder:

dt = New Table( "test",	Add Rows( 2 ),
	New Column( "variable", Set Values( [4, 8] ) ),
	New Column( "N", Set Values( [2000, 3000] ) ),
	New Column( "ratio", Formula( :N / Col Sum( :N )*1000 ))
);
Graph Builder(Variables( Y( :variable ), Frequency( :ratio ) ),	Elements( Bar( Y ) ));

... and the result is 6.4.

so, Graph Builder follows the same lines as the other platforms?

no -- GraphBuilder automatically switches to weight:

... with the previously mentioned impact on other statistics like Median 

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@hogi wrote:

All this definitely makes sense
but nevertheless: surprising when you see it the first time.
and: dangerous - if you don't see it ;) 

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And the counts (previous post), why is the graph misleading?
Freq doesn't have an impact on Counts - neither in Graph Builder nor in Summary Statistics.
[-> I added a comment to the post on summary statistics]