It seems well underbuilt for hay storage, depending on the wood used.. using wood strength of 875PSI Fb, for #2 doug fir, my amateur spreadsheet says allowable bending load per square foot foot on the top floor would be about 20lbs.
That's only around one third a bale of hay per foot..
Switch to dense select structural doug fir at 1900Fb and it more than doubles to about 42 pounds per square foot. Still not great.
Switch to something crummier than #2 doug and it could halve the initial number, perhaps..
It should hopefully be quite easy to reinforce with screw-style steel post jacks if desired.. or wood posts. Do take note of whatever they are transferring the force to at the base..
I personally warrant that the above numbers are worth every cent you paid for them. Most of my knowledge of this math comes from the back of
Rob Roy's 'Timber Framing For the Rest of Us'.