What would you call the idea that theories and knowledge more generally is merely the product of our past interactions with their associated elements? For example, if I were to let go of a ball, one would assume that ball would fall, as every experience of this in the past has led to this outcome. We can’t prove that the ball will (always) fall, we just make the assumption that it will. Is there a philosophy idea that deals with this?
Assuming your knowledge concerns things besides pure mathematics and logic, what you are looking for is empiricism or phenomenology depending on what you are focusing on. If you are interested in how knowledge is related to what we perceive, what you want is empiricism. If you are interested in how mental states, such as belief, is related to what we perceive, you want phenomenology.
Within philosophy realm, knowledge is usually defined as "justified true belief" as here:
For centuries upon centuries, philosophers accepted Plato's theory of knowledge, the view that knowledge is justified true belief. This view is also known as the JTB theory. It's not only a true belief, but also needs to be justified which is the key why Socrates valued knowledge so much. Socrates claimed knowledge is more valuable than mere true belief (say, only by luck you have such some true beliefs) because it is justified. Justification, or working out the reason for a true belief, locks down true belief.
Then how can human beings justify a speculated belief? Usually human beings use inductive or deductive reasoning to help justify a speculated belief at hand. The name of "the idea that knowledge is dependent on past experience" is above inductive reasoning which constitutes most of the body of science, of course deductive reasoning is also applied heavily.
Finally noted, this induction may be fully justified via numerous past experience or experiments, but by no means it's as certain as deductive mathematical knowledge or logical entailment, which is called Hume's Problem of induction. Also in some edge cases like Gettier problem in above first reference, knowledge defined as justified true belief may not be qualified per its own definition like a classic philosophical paradox. So there's still no settled perfect definition of knowledge within philosophy as a solid foundation hoped by positivists or foundationalists yet...