Origins
Money was weighed before it was counted. In the ancient world, payments were made by placing metal on one side of a balance until it matched a standard weight. This is why expense comes from Latin expendere — ex- ('out') + pendere ('to weigh'). To spend was to weigh out.
The Latin pendere meant both 'to weigh' and 'to hang' — a balance hangs, and what hangs can be weighed. This double meaning scattered through English in unexpected ways. A pendant hangs from a chain. To ponder is to weigh thoughts mentally. A pension was money weighed out to a retired soldier. To compensate is to weigh together (com- + pensāre), to balance one thing against another.
The British pound preserves the connection most directly. A pound sterling was originally a pound weight of silver — 240 silver pennies totalling one Troy pound. The currency unit is the weight unit.