When the fish first surfaces after being hooked, Santiago finally gets to see the size of it. The narrator notes that its sword is as big as a baseball bat. Santiago adds that the fish is "two feet longer than the skiff." The narrator then adds that the old man had seen other fish that weighed over a thousand pounds. Santiago had caught fish of this size but never on his own.
Now alone, and out of sight of land, he was fast to the biggest fish that he had ever seen and bigger than he had ever heard of, and his left hand was still as tight as the gripped claws of an eagle.
Since the old man had seen and caught fish over a thousand pounds and since this fish was bigger than any fish he'd ever seen or heard of, we can presume that the fish is well over a thousand pounds. When Santiago finally defeats the fish and begins tying it to his skiff, he remarks that the fish must be over fifteen hundred pounds.