Plate armor is hard, so it's not designed to dissipate that kind of force. If you want to see the kind of protection which is designed to protect against a fall, look at motorcycle gear: it's tough, but generally made of soft material.

Of course, plate armor was supported by layers of other protection, namely chainmail and thick, quilted cloth. Chainmail wouldn't help here, but cloth would. A thick gambeson base layer would help to cushion the fall a little, similar to the way a heavy sweater or a jacket would. This would be the only piece which would provide any actual cushioning. Keep in mind that this cushion would be concentrated mainly on the upper body, and not so much around the head or legs. If Biff fell and hit his head, it would not end well for him.

The metal pieces(plate and mail) would probably serve three minor roles:

• They would protect Biff from cutting himself from falling.
• They might help distribute the force a little more evenly across the gambeson in case Biff didn't fall on flat ground.
• They would slightly restrict Biff's range of motion, making it a little less likely for Biff to break or dislocate a limb. (This would be very slight, because it was really important for medieval warriors to maintain a good range of motion in armor) More importantly, Biff is less likely to get whiplash in his neck.

A lot of the features of plate armor are completely useless against a fall. For example, rounded or angled plate is meant to deflect a blow instead of taking it directly, but it's tricky to deflect a planet. Also, plate armor has a lot of openings and weaknesses in order to make sure you can fight while wearing it, but Biff won't care about mobility when he's falling to his death. It's also worth mentioning that one common way of defeating plate armor is to hit it with blunt, heavy force, like a polehammer. Plate armor is not meant to stop blunt trauma.

Biff would definitely be cushioned a bit, but would he be better off without armor? Well, that's hard to say.

As Galileo proved, heavy objects fall at the same speed as light objects. However, remember that Force = Mass * Acceleration. Greater mass means greater force, and all of that energy needs to go somewhere.

Let's say Biff weighs 80kg normally, and he's wearing 35kg of armor, including fabric, mail, and plate. The protection that Biff receives from the armor would have to outweigh the added force from those 80 pounds.

Acceleration due to gravity is 9.8 m/s^2, so we can write the equations as:

Force = mass * acceleration
Force(naked) = 180kg * 9.8 m/s^2 = 1764 newtons
Force(armored) = 215kg * 9.8 m/s^2 = 2107 newtons
Force(armored) - Force(naked) = 343 newtons

We don't know how far Biff is falling, but since the force of gravity represents not just velocity but acceleration, his extra mass is going to add up very quickly as height increases. Let's see how much it adds up. Since you said that he's falling from the second story, let's assume he's about 5 meters above the ground. We can plug in the height to find how long it takes him to fall:

time = sqrt((2 * height)/gravity)
time = sqrt((2 * 5m)/9.8 m/s^2) = 1.020 seconds

For the sake of curiosity, we can use that time to figure out how fast he's going when he Wile E. Coyotes into the ground:

velocity = time * gravity
velocity = 1.020s * 9.8 m/s^2 = 9.996 m/s

If I take his force and multiply it by 1 second, I will get his momentum.

    Momentum = force * time
    Momentum(naked) = 1764N * 1.02s = 1799.28 kilogram meters/second
    Momentum(armored) = 2107N * 1.02s = 2149.14 kilogram meters/second
    Momentum(armored) - Momentum(naked) = 349.86 kg m/s

My guess is that he's going to want that armor less and less if he falls from greater and greater heights. If we changed the height to 10 meters, then we'll get the following values:

time = sqrt((2 * 10m)/9.8 m/s^2) = 1.4 seconds
Difference in momentum = (2107N*1.4s) - (1764N*1.4s) = 1187.2 kg m/s

By doubling the height, we more than triple the difference in momentum.

And at a certain height, your only real hope of surviving is to let your body go limp like a ragdoll so that it's not tense on impact. That's going to be harder with armor on.

(As a side note, there are also ways of training yourself to break falls safely from regular heights. I suspect this would be much harder to do in armor, which is another strike against it)

Here's what I'd say: Biff should take off everything that isn't made of cloth or leather, except for his helmet. That way, he gets most of the cushion while shedding most of the weight, and he gets some metal coverage where it's most useful. He'd be better off with a breakfall and a bike helmet, but fuck Biff; he's just an understudy.

edit: More math!