Origins
The English word 'cost' has an etymology rooted in the act of standing still. It descends from Old French 'cost' (expense, outlay), from the verb 'coster' (to cost), from Latin 'cōnstāre' — a compound of 'con-' (together) and 'stāre' (to stand), from PIE *steh₂- (to stand). The Latin verb 'cōnstāre' meant literally 'to stand together,' but its semantic range was wide: it meant 'to be settled,' 'to be established,' 'to be consistent,' 'to be agreed upon,' and — crucially — 'to be fixed at a certain price.'
The path from 'standing' to 'costing' is not immediately obvious, but it makes sense once you understand Roman commercial language. When a price was agreed upon in the marketplace, it 'stood firm' — it was fixed, settled, no longer negotiable. 'Quanti cōnstat?' meant 'How much does it stand at?' — i.e., 'What price has been established for this?' The metaphor is of a price that has stopped moving and now stands in place. From this use, 'cōnstāre' narrowed in Vulgar Latin to mean simply 'to cost,' and this narrowed sense passed into Old French and then into English.
The PIE root *steh₂- (to stand) is one of the most productive roots in the entire Indo-European family. Through Latin 'stāre,' it generated an enormous vocabulary: 'state' (how things stand), 'station' (a standing place), 'stable' (standing firm), 'statue' (something standing), 'status' (a standing, a condition), 'stature' (how tall one stands), 'establish' (to make stand firm), 'constant' (standing together, unchanging), 'constitute' (to make stand together), 'circumstance' (things standing around), 'substance' (what stands beneath), 'distance' (standing apart), 'instance' (standing near, pressing), 'obstacle' (something standing in the way), and 'prostitute' (standing before, i.e., offering oneself publicly).
Greek Origins
Through Germanic, the same root produced 'stand,' 'stood,' 'stead,' 'steady,' and 'steed.' Through Greek 'histánai' (to make stand), it produced 'ecstasy' (standing outside oneself), 'system' (things standing together), and 'apostasy' (standing away from). Through Sanskrit 'sthā-,' it produced 'stupa' (a mound that stands).
The word 'cost' itself developed additional senses in English beyond the purely monetary. 'At all costs' and 'at the cost of' extend the meaning to any sacrifice or loss — time, effort, health, life. Legal 'costs' (the expenses of a lawsuit) date from the fourteenth century. 'Costly' (expensive) appeared in the same period.
The relationship between 'cost' and 'constant' deserves emphasis. Both are from 'cōnstāre,' but they preserved different senses of the parent word. 'Constant' kept the sense of 'standing firm, unchanging' — what is constant does not waver. 'Cost' kept the commercial sense of 'standing at a fixed price.' They are the same Latin word that diverged into two English words through the specialization of meaning.
Legacy
There is a quiet irony in the etymology: 'cost' implies fixity and firmness, yet costs in practice are anything but fixed. Prices fluctuate, inflation erodes value, and what something 'costs' depends on when and where you buy it. The word preserves a vision of settled, stable pricing that the market has never quite delivered.