OK, here's the deal from a local: Right now, it's hot and humid - May will not be any different. When it's overcast, it's not so bad, but definitely not sweater weather (or even jeans!) When the sun is out, it's downright painful.
My advice: pack a light item to wear indoors. Right now our AC is cool, so I might wear a tee and jeans or sweats inside. Disney's AC in the hotel rooms tends towards the muggy if cool side of hotel ac.
For outdoors/parks stuff, pack your normal summer gear cause it's hot down here! And not Canada wimp hot - this is the real thing, hot and humid. (Or course, I don't own anymore close-toed shoes and barely any sweaters anymore, so I'm one to talk!)
Jeans, sundresses, shorts, tees and good broad-billed hats will you suit you fine and there really isn't any need to bring anything warm.
In the evening and morning it is a little (A LITTLE cooler.) Consider this: Usually, in the morning you are heading toward the parks, where it will eventually warm up, no? So don't bother bringing anything warm like. If you are eating/riding rides in the parks, the a/c will be a great break from the heat. In the evening, if you are going to a nice sit-down, you may want to change into some more respectable clothing, so maybe pack a few khakis /polos/cargos/"resort casual" for the boys and sundresses/maxi dresses (I live in those!)/cardigans/khakis for the girls.
And DON'T forget your sunscreen. I know I always say that, but in the parks, I constantly see Northern "lobsters" because people from up north forget their sunscreen and to apply it. If it's sunny out, put it on before you leave, and apply it liberally. If it is NOT sunny out, apply it before for you leave for the parks as well. Not putting it on when it's overcast is one of the main mistakes people make, and they pay for it. And don't forget your shins, top of your feet, hands, and other crevices that you don't think the sun while shine in cause it will get in there! So get yourself a lot of plant-based sunscreen (Badger is pretty good) and dip everyone in you group in it, OK?

And re-apply. Then apply some more.
One very last thing - consider buying runners glide. I'm not fat, but since I wear skirts a lot, I tend to get friction burns from the heat (walk + sweat = ouch.). The runners glide is great for helping stop those burns. It comes in a deodorant like container and it's a great purchase for the parks. Clear, non-sticky, and no smell.
Hope all that helps!