"In a way, I feel like I should be a big enough person to be okay with this, but I'm not."
One of the distinctions I like to draw strongly is between "nice" and "good". They are not the same, and at times, are actively at odds with each other.
It is certainly nice to give away your software to everybody, unconditionally, and not be bothered if your code does happen to end up being a fundamental component of some multi-billion-dollar company that gives you nothing.
But I'm less convinced that's necessarily good. In a world where you must live under the assumption there are bad actors, I think it's OK to put into your license that they can't necessarily do that. It is good to prevent the exploitation of anybody, and that goodness extends to preventing the exploitation of yourself, even if you also clearly have direct personal interests of your own.
I don't think "being comfortable with being exploited" is a component of "being a big person".
On the other hand, we often bring to mind mental examples of software where we slaved away for years and years to bring some unique new product to the world, only for it to be stolen by the big bad corporation for no compensation. My verbiage above about "exploitation" probably brought that to the reader's mind as the topic of discussion. If that happens, yeah, it's bad. On the other hand, that's not really the dominant case for software. There's a lot of open source put out there that's just a few day's work, which is still plenty valuable at scale, but if someone took one of these little things and incorporated it into their product, it's not really that big a deal.
I have several such small little things and they're all BSD. If a big corporation did somehow walk off with one of them, I'd legitimately be flattered, because I know that while it may have saved them a bit of time, it certainly isn't a core component of their product and had they needed to implement something themselves it would have been a trivial fraction of their time. I know I can say I'd be flattered because to some small extent, this really has happened, and I really was flattered and appreciative, so I'm not just hypothesizing about my future emotional states. I'm well aware on all levels that my ~two weeks total effort on the project in question, which I mostly did for my own purposes and for which the open source effort was essentially a bonus, doesn't entitle me to significant compensation for a product whose size is measured in person-decades.