Weighted Unknowns let you specify the relationship that each payment has to another. For example, you may solve for two unknown payments where one is an unknown amount and the other is twice the unknown amount.
Weighted Unknowns are useful where you have 2 payments upfront followed by a series of regular periodic payments. Typing 2X in the Amount field (or typing 2 and right-clicking in the Amount field, and then choosing Weighted Unknown from the context menu) would specify the two upfront payments. On the next cash flow line, the remaining periodic payments would be specified by typing 1X or [U] in the Amount field.
When calculated, the first payment will be twice the amount of the remaining payments.