You pay for going out of a channel. On the first hop, you don't pay because it's your channel. On the second hop, you pay B the fees set on channel BC. See more here.
You don't pay B only when you pay B directly, when B is making you a LN invoice and you pay him without any other route. But when you use B to route your other invoice to C, you will pay him the fee for routing that tx. https://docs.lightning.engineering/lightning-network-tools/lnd/channel-fees
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