The cost of transactions is independent of the amount transferred. Rather it depends on the weight of the transaction, the current blockspace demand, and the urgency the sender wants to see it confirmed.
A transaction's weight is calculated from the byte count of its serialization. Non-witness data counts at a factor of 4, witness data counts at a factor of 1. Each transaction must have at least one input and one output, transactions with more inputs and outputs will weigh more. (See e.g. this overview of the weights of different output types.)
Transactions compete for the block weight they occupy in a block. Rational miners will prefer transactions with the highest feerate (fee per block weight) to maximize their mining revenue. A transaction's fee can thus be interpreted as a bid for a specific amount of block weight. If there are a lot of transactions waiting for confirmation, a sender might need to offer a higher feerate to see their transaction confirmed quickly.
Nodes generally do not relay transactions that pay feerates lower than 250β―sat/kwu (or 1β―s/vB), and miners usually do not include transactions in their blocks that pay less than this "minimum feerate".
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