"Net neutrality" is a problematic term because it seems to mean different things to different people depending on their perspective/motive. For instance, I've seen arguments that T-Mobile not charging for SD video streams is net neutral because any company is allowed to get into the program.

In its strictest (and IMO, most useful) sense, "net neutrality" is the concept that data is data is data. It doesn't matter whether it's carrying video or whether it's carrying text, whether that comes from Google or whether it comes from the server in your basement, or whether it's being transferred at 11am or at 11pm.

IMO that definition is the most useful because it's the clearest - anything else ends up getting into some debate about why this applies and that doesn't. I'd very much like to keep my neutral internet connection - the creeping preferentialism on my cellphone connection is not welcome.

One simple example would be Verizon only allowing free nights and weekends to certain services. For example, Verizon allows free night and weekend data usage for Hulu but not for any other streaming video services. This is a huge loss to Netflix, Amazon Video, YouTube and any other streaming services, including those whom don't yet exist since it would be harder to gain users due to the newer service "using more data" than using Hulu (read: the Verizon subsidized alternative).

At least, I'm assuming that's what OP meant. Not simply that "free nights and weekends" would be anti-net neutrality on its own, but that it could very easily be made more proprietary than it initially sounds. And we've seen it done in the past when free nights and weekends were were restricted to those within your telco, the x-amount of people within your network that are free to call[I believe AT&T made it 10?], the free mobile to mobile that was eventually restricted to free mobile to mobile only within the same telco again, etc., etc.

Smaller or up-and-coming carriers can't always afford to give away their service for free, whereas larger carriers can offset the losses more easily.

Edit to clarify, it's more "anti-competitive" than "anti-net neutrality"