Clever, but unlikely
In order for Catapult to work, it requires:
one object weighing 1 to 5 pounds within range that isn’t being worn or carried.
This is the requirement that Delayed Blast Fireball must meet. The question is: Does it?
Delayed Blast Fireball isn't explicit in the definition, but it does state:
A beam of yellow light flashes from your pointing finger, then condenses to linger at a chosen point within range as a glowing bead for the duration.
How much does a bead of light weigh?
In order for that bead to qualify for Catapult, it must be at least one pound and less than five pounds. As Dale M states, that's likely a DM call. But how should the DM approach?
Well, it's a beam of light that condenses into a bead. How much does a bead of light weigh? I'd think that a bead of magic light does not weigh anything, but another DM may believe otherwise. Then it's a question of does a bead of light weighs more than 1lb. Even if it did have a mass, it's unlikely to weigh more than 1lb.
Without meeting the weight requirement, you can't use Catapult to launch the Bead for extra damage (pending the save failure).
Throwing the Bead
There is another option for interacting with the Delayed Blast Fireball:
If the glowing bead is touched before the interval has expired, the creature touching it must make a Dexterity saving throw. On a failed save, the spell ends immediately, causing the bead to erupt in flame. On a successful save, the creature can throw the bead up to 40 feet.
This does imply that it can be handled, but it doesn't answer weight or anything else. Ultimately, this is a magic bead made of condensed light and it does not necessarily mean it has mass. It just means that you can throw the magic bead. If a DM does rule that it has mass, then it still needs to weigh more than 1 lb (see discussion above on weight of condensed light.)
Blinking to the ethereal plane does not halt the fall.
Nothing within the Blink spell or the Ethereal plane's description suggests that you lose momentum during your short existence within the Ethereal plane.
Thus, at the beginning of your next turn, your falling distance in not set to 0. Once you hit the ground, you take the full damage associated with a 510' fall.
A 'lenient' DM may reasonably apply the optional rule for falling from XGE because while you're on the ethereal plane you can basically hover/fly.
If you’d like a flying creature to have a better chance of surviving a fall than a non-flying creature does, use this rule: subtract the creature’s current flying speed from the distance it fell before calculating falling damage. This rule is helpful to a flier that is knocked prone but is still conscious and has a current flying speed that is greater than 0 feet. The rule is designed to simulate the creature flapping its wings furiously or taking similar measures to slow the velocity of its fall.
But that won't help much in this scenario because you would still take the falling damage associated with a 480' fall.
However...
The Ethereal Plane also disobeys the laws of gravity; a creature there can move up and down as easily as walking.
...if you ready your action to move on the Ethereal plane you could reasonably halt your fall.
This is similar to what a flying creature can do according to XGE's optional rules for falling:
If you use the rule for rate of falling in the previous section, a flying creature descends 500 feet on the turn when it falls, just as other creatures do. But if that creature starts any of its later turns still falling and is prone, it can halt the fall on its turn by spending half its flying speed to counter the prone condition (as if it were standing up in midair).
Best Answer
TLDR: While levitating, a creature is not falling, therefore the rules for falling damage cannot be applied.
To answer your question, lets look at the rules for the two things involved here: Levitate and falling
Levitate (PHB 255)
First partial problem with the idea is that slamming the target into walls doesn't work, because the caster can only change altitude.
Falling (PHB 183)
Here is the big problem. Nothing in the description of falling says anything about acceleration, or gravity, or the like.
Instead, it says "At the end of a fall". While a fall is a change in altitude, a change is altitude is not necessarily a fall.
I would rule that while the levitate spell is active, no fall is taking place, and so no falling damage can occur.
Obligatory: 5e is not a physics simulator.