The obvious objection to esse est percipi is intermittence: things would flicker out of existence whenever no finite mind attended to them. Berkeley meets it head-on. Sensible things do continue when I do not perceive them — therefore they exist in another mind, one that perceives them always.
Berkeley thinks this yields a demonstration cleaner than the argument from design. The traditional proof reasons from the order of nature to a wise contriver; Berkeley reasons from the bare existence of the sensible world to an infinite perceiver, since anything sensible must exist in some mind, and the world is not sustained by ours.
The theological payoff is intimacy. Where the materialist sets an inert substance between us and God, Berkeley removes it: the ideas of sense come to us directly from the divine mind. God is not inferred from distant effects but encountered continuously in every perception — the constant author of the world we wake into each morning.
The proof from the continued existence of sensible things is given in the Second and Third Dialogues.