Sum weight based on dropdowns

Hello,

I'm looking for a formula to sum up the weight of a wall based on the variables input through several dropdowns. I found several articles online about adding multiple values based on a single dropdown, but not how to add multiple values based on multiple dropdowns.

On the attached, if you change a dropdown, the formula should go to sheet 2, find the weight, and add it all together.

The first line is a desired result of manually adding the weights up, but not dynamic in that when you change the dropdowns, the weight doesn't update.

Any help is appreciated! Thank you!

EDIT: Sorry, I should have said, I tried the "=SUMIFS(Sheet2!I3:I51,Sheet2!B:B,Sheet1!B2,Sheet2!B:B,Sheet1!C2... etc.) formula and I get a "#VALUE" error... I'm guessing because each criteria range is the same range?