1. To use a particular payment method when making a purchase. Can I pay by card, or do you only accept cash? I hope they let me pay by check.
2. To make a payment (to someone) by certain day, date, or time. In this usage, a noun or pronoun can be used between "pay" and "by" to specify who is being paid. The deadline was originally last month, but they're letting me pay by the end of next week due to my circumstances. I promise I'll pay you by the end of the day!
pay by something
1. Lit. to use something as a medium of payment. Will you pay by cash or check? The bill was paid by check.
2. Fig. to pay by a certain time. You will have to pay by the end of the month or we will cancel your lease. I promise I will pay by the end of the month.