Let's say you want the following:

Product A ships for $3.75 ... set the Product Weight to 3.75 ...

Product B ships for $2.25 ... set the Product Weight to 2.25 ...

Product C ships for $1.00 ... set the Product Weight to 1.00 ...

Order 1 of Product A, 1 of Product B and 10 of Product C:

Shipping is:
Product A 1 x 3.75 = $3.75
Product B 1 x 2.25 = $2.25
Product C 10 x 1.00 = $10.00

Total Shipping is $16.00 if the Unit Rate is set to 1.00 on the Per Unit perweightunit shipping module ...