Lime will help, but you still need your soil tested so you know how much.Thanks for the info guys, a lot to digest and research further. The hay field isn't massive (non industrial), only 50 acres.
I'm going to add some lime to see if that helps a little bit.
One natural way is to burn the field. It will burn up the seeds from the weeds and help to keep your weed problem down. The grass will grow back.