Sum on Multiple Sheets based on Single Condition

I have a spreadsheet that I need to sum numbers in separate columns on different sheets, based on a common number that is shared between each sheet.

There are several columns of numbers, each column representing a bar size. I used random numbers to represent weights.

For example, I need the sum of all the "3" bar weights from each sheet, and displayed in cell B2 on the Summary page, and so on.

You will better understand if you look at the attached spreadsheet.

We are using Excel 2013.

Thanks,
Chris

Please manually enter the results you are expecting on the summary sheet and explain in words your calculations for cells B2 and C2.

Please try at B2 and drag down

=SUM(INDEX(CHOOSE({1;2},Sheet1!$B$3:$L$3,Sheet2!$B$3:$L$3),,MATCH(A2,Sheet1!$B$2:$L$2,)))

Please try at B2
=SUMPRODUCT(SUMIFS(INDIRECT("sheet"&ROW($A$1:$A$2)&"!B3:L3"),INDIRECT("sheet"&ROW($A$1:$A$2)&"!B2:L2"),A2))

Blue is your sheet name, if you have 50 sheets, change Red "2" to 50

Please try

=SUMPRODUCT(SUMIFS(INDIRECT("sheet"&ROW(INDIRECT("1:"&SHEETS()-1))&"!B3:L3"),INDIRECT("sheet"&ROW(INDIRECT("1:"&SHEETS()-1))&"!B2:L2"),A2))

SHEETS() give all sheet count and -1 for the summary sheet.