The discussion in the Theaetetus really takes off when Theaetetus tries out his first definition of knowledge, suggesting that it’s “nothing other than perception” (οὐκ ἄλλο τί ἐστιν ἐπιστήμη ἢ αἴσθησις) (151e). Socrates immediately equates this definition with the sophist Protagoras’s claim that “Man is the measure of all things” (152a). The idea is this: if perception is “being appeared to thusly,” and if anything that appears to us is true, then it’s reasonable to say that we — perceivers — are the measure of all things. Of course, Socrates is already implicitly relying on a relaxed sense of perception — Protagoras’s relativism includes a great deal more than sense-perception, but extends to judgments about necessary truths, moral truths, and so on. But if you grant the relaxed sense, this is probably OK.
Socrates goes on, in paraphrasing Theaetetus’s definition, to put it thus: “whatever things appear to me, these things are for me; and whatever appears to you, is for you” (οἷα μὲν ἕκαστα ἐμοὶ φαίνεται τοιαῦτα μὲν ἔστιν ἐμοί, οἷα δὲ σοί, τοιαῦτα δὲ αὖ σοί) (152a). This is a more surprising shift yet: from the thesis that knowledge is perception, Socrates has arrived at the thesis that being is perception, which he will go on to explicate in terms of Heraclitus’s metaphysics of radical flux (cf. 152d-ff.). Is this right? Well, if it were the case that anything perceived (e.g., anything that seems to you to be true) counts as knowledge, then it’s hard to say how we would arrive at an account of what is in terms of anything other than perception — if there were an objective, external world, it would be unknowable. The Protagorean is a Kantian without the categories, locked in a phenomenal world that can’t be evaluated objectively or interpersonally.
Socrates has deduced a relationship of entailment: If Protagoras, then Heraclitus. But we can’t reverse the inference (the fallacy of affirming the consequent): it doesn’t follow from Socrates’ inference that, If Heraclitus, then Protagoras. The thesis, “being is being perceived” (esse ist videri), which Berkeley would later endorse, doesn’t entail thorough-going relativism in the way that relativism entails the Heraclitean metaphysics. Why not? Well, Berkeley’s initial motivation for the “being as perception” thesis is simple: if I perceive that an oar looks crooked when dipped into water, I learn something true about oars in relation to water (under ordinary perceptual conditions, of course). The idea of oar-ness includes in it this property of appearing bent when dipped in water. But that doesn’t mean that I can’t be mistaken in my beliefs. Say that I formed the belief that the oar would continue to appear crooked when pulled from the water — if so, I’d be mistaken, because I had made a false inference. The appearance of oar-crookedness is indexed to being-underwater; a different set of appearances attached to oars in open air. (For discussion of oars and water, cf. Berkeley, Three Dialogues 3.2.5.)