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(Not a professional physicist.)
My understanding is that we have a very good model for how gravity should work, and we've used that model to predict a lot of things we can observe. A few I can think of offhand:
Physic student here, so not a full professional yet.
I just wanted to add to this nice explanation that using the models of how we expect gravity to behave, we theorized the existence of black holes way before observing them. And not just black holes, but many other observations about the nature of our universe were theorized before we saw them. Like light bending.
That's how good the math was, that the models keep proving to be accurate as we observe more of our universe. I find that so cool :)
And most of the math was from Einstein. No wonder he was that famous already during his lifetime and his name became synonymous with intelligence. Some of his predictions only got experimentally proven recently (gravitational waves).
Also, just to add to this. Regarding point one, photos of the stars taken during a total eclipse show shifts in position consistent with their light being bent by the relatively modest mass of our own sun.