They say big websites will pay for fast delivery and small websites will have their data delivered slower.
I have a small website. I already pay for bandwith. What will change? Will I be charged more for fast bandwith?
Should the same go for people? Are you looking forward to possibly seeing ISPs nickel-and-dime you to death, e.g. with "packaged internets" products that limit the sites you can visit based on how much you pay? - https://news.ycombinator.com/item?id=15934044
ISPs may prioritize traffic for services like Netflix to reduce latency for their services. Yes, this may mean traffic for standard text-and-graphics web sites get slowed down a bit, but latency on those kinds of sites do not degrade the user experience as latency on streaming video.
(I remember when the Sega Dreamcast launched, Sega also launched an ISP which somehow prioritized Dreamcast game traffic so that your online Dreamcast games had less theoretical latency. I suppose "gamer ISPs" could become a thing again too.)