Can the small air elemental move him 100-feet because the spellcaster is weightless? Or are their other factors to consider?
Levitate allows you to move yourself, another creature, or an object up and down as you wish. A creature must be willing to be levitated, and an object must be unattended or possessed by a willing creature. You can mentally direct the recipient to move up or down as much as 20 feet each round; doing so is a move action. You cannot move the recipient horizontally, but the recipient could clamber along the face of a cliff, for example, or push against a ceiling to move laterally (generally at half its base land speed).
A levitating creature that attacks with a melee or ranged weapon finds itself increasingly unstable; the first attack has a –1 penalty on attack rolls, the second –2, and so on, to a maximum penalty of –5. A full round spent stabilizing allows the creature to begin again at –1.
Nothing about levitate makes the recipient weightless. It just affords them magical flight on the vertical axis. The levitating creature still has his full weight.
A small air elemental has a strength of 12. There is a rule (which for the life of me, I cannot find to quote right now) that a creature cannot fly if carrying more than a light load if flying with wings, or more than a heavy load when flying magically. Since air elementals obviously aren't using wings, I'm going to move towards magical flight. With a strength score of 12, they can carry 130 pounds. One might be able to argue that the air elemental is "dragging" the levitating character, and that the lack of friction makes "favorable conditions", and so the upper limit of that would be 1300 pounds.
All that said, depending on how the GM wants to rule weight limits for flying creatures, you might have no problem towing along a 2/3rds of a ton, or might struggle to pull a full grown human.
Other factors to consider would be convincing the air elemental to work for you. From their entry: "Primitive and territorial, they resent being summoned or doing the bidding of mortals, and much prefer to spend their time on the Plane of Air, swooping and racing through the endless skies." To summon one and ask it to be a glorified draft animal would probably anger it.
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Can the small air elemental move him 100-feet because the spellcaster is weightless? Or are their other factors to consider?
The spellcaster weighs the same as before, he's just 20 feet above the ground. As a Small creature with STR 12, the air elemental can carry 32 pounds at a speed of 100 feet or 97 pounds at 70 feet. I'd say a load floating above the ground is a favourable condition for dragging, so the air elemental can drag up to 975 pounds at 5 feet per full round.
You cannot move the recipient horizontally, but the recipient could clamber along the face of a cliff, for example, or push against a ceiling to move laterally (generally at half its base land speed).
With this a a base line, I would allow the air elemental to move you at 1/2 your base speed.
Other factors to consider would be convincing the air elemental to work for you. From their entry: "Primitive and territorial, they resent being summoned or doing the bidding of mortals, and much prefer to spend their time on the Plane of...
You can take one as an improved familiar.
This actually game up in my game - I ruled that the elemental could tow the wizard around as if he was a medium load (i.e. 70') but only horizontally. So he'd have to move up and down as a move action on his turn, and then the elemental would pull him around on it's turn (which happened immediately before or after, but not during). It made for some weird movement, and I'm not sure I'd allow it again, but it does work.