The shipping module Per Unit perweightunit is designed to allow the shipping cost to be entered in the Product Weight ...

The total weight of the order is then multiplied by the Rate in the Per Unit perweightunit shipping module ...

This would allow you to enter the Product Weight as 2.50 ... Buying this Product would then charge:
Qty 1 x 2.50 = 2.50
Qty 2 x 2.50 = 5.00
Qty 3 x 2.50 = 7.50

Then on the next Product, entering the Product Weight as 1.00 ... would then be:
Qty 1 x 1.00 = 1.00
Qty 2 x 2.00 = 2.00
Qty 3 x 3.00 = 3.00

Add 2 of the first Product and 3 of the second Product and the charge would be:
2 x 2.50 = 5.00
3 x 1.00 = 3.00

with the total shipping charge being: $8.00

To use this method, you should set the settings in the Shipping/Packaging for ...
Maximum Weight: 5000
Both Tare settings to: 0:0