If you want honey quick there are a few tricks. I don't have to play those games, since where I'm at our biggest harvest can be in Feb. when the eucalyptus are blooming. Then we don't get rain, so summer isn't much fun for beekeepers. We often go 180 days without rain during spring and summer.
What you can do in Arkansas etc.. is to feed the bees sugar water early in the year, so as to stimulate egg laying and the "drawing out" of new comb. The amount of feed they have available causes them to either lay more or less eggs, and the amount of sunlight doesn't have any more to do with it that sunlight cause yeast in the must to multiply (although you're right, they can foretell weather, but that's a story for another time).
So if you have lots of flowers say in April (am I guessing right for your area?) and you've fed them for 6 weeks or so before that, you should have no trouble getting 200 pounds or so the first year, provided you have a good queen, etc....
Remember, the brood only lasts for 21 days, at least the worker brood, so it's not something that you can save up from one year to the next. The bigger things are
1: make sure you have lots of bees when you have lots of flowers
2: it takes 8 pounds of honey to make one pound of wax, so try to make sure the bees have comb that's already drawn out when the "flow" ( i.e. peak production of nectar by your target flowers)
Here, if we get good rains coupled with lots of warm sunny days during the winter, I have gotten 300 pounds from good hives, and there are places in the US where beekeepers can do even better with good hives, but 100 pounds is more realistic for an average. And if you let nature take her course and just use queens the hives produce themselves, you may only get 25 pounds.