According to Catapult's description, the spell is limited by the weight of the object with some variance based on the level in which the spell was cast. With the spell Levitate, could you interpret this to mean that an object under the effects of Levitate weighs effective 0 and then be subjected to the effects of Catapult?
Levitate does not change the weight of an object
Just because an object is held aloft doesn't mean it is weightless. If you pick up a rock, does it become weightless until you put it down? Nothing in the text of the Levitate spell changes the weight of the levitated object. There are spells that can change the weight of something, such as Enlarge/Reduce, but Levitate is not one of them.
Hence, if you levitate a 500-pound object and then attempt to cast Catapult on it, the spell will fail, because the target object weighs more than 10 pounds.
On a valid levitated target, Catapult works normally
Catapult works on
one object weighing 1 to 5 pounds within range that isn’t being worn or carried.
If such an object is currently under the effect of a Levitate spell and suspended in mid-air, that object is neither worn nor carried, so it remains a valid target for Catapult. Furthermore Levitate does not hold the target in place or in any way prevent it from being moved, so nothing inhibits the effect of Catapult when cast on this object. If you do this, the object will start from a point in midair and move 90 feet in the designated direction, stopping at the first thing it hits, where it will once again remain suspended in midair.
This initially started as a response to Ryan's answer, but I think that this explanation requires a full answer.
Levitate depending on your DM's ruling, could make an object weightless
In scientific terms weight is a definition of force, not mass. The text for Levitate does not specify the exact mechanism at play, so, if your DM rules that the Levitate spell simply removes the force of gravity on a creature, Levitate would indeed make the object weightless.
Either way, you still cannot use Catapult on the object
Catapult's definition has the following qualifier:
Choose one object weighing 1 to 5 pounds
As a Levitated object is weightless (meaning it weighs 0 pounds), it cannot be used as the target for Catapult.