You misunderstood the parabola part. Here's a list of jump arc gifs:
https://imgur.com/a/9Dj5F
With a full jump, Meat Boy's jump is a lot more "floaty" as it has more airtime and slower descent.
But Meat Boy has a mechanic where when you release jump before the peak, you drop down directly, cutting the parabola short down to a seesaw.
(Original) Mario on the other hand has a mechanic where as long as you hold jump, gravity is reduced on the way up. At the peak of his jump or when you release jump, gravity suddently becomes heavy, making him drop like a rock.
With Mario, the two half parabola are roughly decided when you start the jump, and you can only fine-tune it. Mario has good air-time but low air-control because he is "
slippery" (low horizontal accelleration), so air-control is difficult.
Meat Boy has very high horizontal acccelleration, so he has a lot of air control (you can change direction during a jump). This means that his levels are designed so that you have to control the jump all the way trough.
Another extreme are classic Megaman where he has infinite horizontal acceleration (but low top speed). We often call this "
sticky" because he starts and stops immediately (no slowing down or accelerating). Where you land becomes 100% linked to your immediate button presses, rather than a composite of button presses over time.
Due to the gravity increase on the way down that gives him a "weighty" feeling, I wouldn't call Mario "floaty".
"Floaty" is for games like LBP with low vertical speed, where it can take aggravatingly long to rise/fall. I don't know exactly what's the issue (symmetrical parabola? impulse-based? or just slow descent?).
Not all jumps use parabolas. For example as said
in a previous post I might be wrong but I think Meat Boy has constant speed on ascent to make the height more controllable, and the top is on a timer.
