"Average" doesn't mean very much in this case. I suppose you could say the average is about 1,000 pounds or so, since hay bales can range from as little as 40 or 50 pounds to well over 2,000 pounds.
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That really depends on the content of the square bale, whether it is comprised of straw or hay and the moisture content of that bale. On average a large square bale will weigh around or over half a ton.
It depends on the size of the bale, how the operator has the baler set up, and the type and quality of hay in the bale, but it should be somewhere between 800 and 2,000 pounds.