The transition is abrupt because you're moving the card uniformly. The uniformity means that you get a greater relative change in density in the light areas than the dark:
- outside the burn, you have 12s
- in the middle of the burn, you have 24s
- at the edge, you have 36s
So the middle of the burn is twice as dense as the unburnt, while the outside corner is only 1/3 denser than the middle of the burn. The closer to the unburnt area you get, the steeper the apparent density gradient becomes.
The next thing that's making it MUCH worse is that you're burning with #00 a print made at #2.5. At #2.5, your unburnt highlight has practically zero density, but the #00 will burn the highlights in REALLY quickly. So in terms of the density achieved on the paper, you're talking more like 6s of base exposure and 24s of burning. So the inner bit of gradient is 6s -> 18s (factor of three) while the outer bit of gradient is 18s -> 30s (factor of < 2). I almost never burn at a lower grade, I generally only burn at the same or higher grades.