Suppose the pressure is 2000 psi at the bottom of the sea. You take a standard bathroom scale down there, to the bottom, say 100 square inches.
What would it read for weight?
The weight of the water column, ie 2000 x 100 pounds? Or twice that as it’s being pushed from both the bottom and the top, ie it’s being pushed together?
Or would it read zero?
Zero.
Unless it was 100% waterproof, and left unopened since being at surface conditions. In which case it would have been crushed at some point during the descent.
Tris
The ideal scale (the one that can deal with the water and handle the pressure) would read the weight of the water above it (i.e. pressure X area).
It would not read twice this for the same reason that when a 150-lb person steps aboard, it reads 150 lbs even though it’s being pushed together (by the person above and the bathroom floor below).
I agree with Triskadecamus - assuming that the scale isn’t sealed, it would read zero. The force on the platform of the scale caused by water pressure would be met by an equal force on the other side of the platform, caused by the same pressure.
If you want to get picky, the gravitational field at the bottom of the ocean is slightly weaker than at sea level, and if your scale is sensitive enough it could detect this. I don’t think this is what the OP was asking, though.
Ditto Triskademus. On the earth’s surface you are already submerged under air weighing 15 pounds for every square inch of land, and the scale doesn’t register something like a ton for that, either.
Picture a balance scale - the kind with two pans on either end of a beam. Now picture that on the bottom of the ocean. Why would one pan be lower than the other?
It wouldn’t - since both are exposed to the same forces.
A bathroom-style scale uses a spring (or something similar). If you seal it to make it waterproof, it tends to be called a pressure gauge and typically reads force divided by area.
Not a direct answer to the OP, but just in case you need it, here’s a depth/pressure calculator for you.
that’s because the scale is calibrated for air pressure. at the bottom of the ocean, it would register the weight of the water as well.
the platform is counteracting the downward pressure but the scale isn’t showing the net force (zero) but rather only the downward component, which is the water weight + whatever weight you’re measuring.
just because the ocean scale and the land scale is balanced doesn’t mean they’re equal. two kgs on both sides balances a scale just as well as 5kgs, 10kgs, etc.
Do check the list of scales! 
Xema and pancakes3 are correct. Everything else is nonsense.
The scale weighs the downward component of weight only. When you step on it on the bathroom floor, it doesn’t register the normal force upwards from the floor and tell you that you weigh 0 lbs. In this case forces are balanced, as they should be since neither you nor the scale are accelerating, and the scale doesn’t register 0 lbs.
It is the same with a spring scale. When you hang a weight on a spring scale it doesn’t register 0 even though the spring force is balancing the gravitational force.
It will measure the 2000 psi X 100 square inches.
Wrong.
Obviously.
If this were true, the scale would measure 14.7 psi x 100 in^2 at sea level.
Scales aren’t sealed. Therefore, there’s no net pressure on the sensor.
What is being discussed here is the difference between gauge (PSIG) pressure and absolute pressure (PSIA). Gauge pressure is differential. Most pressure gauges read this way, because it is the most common pressure people are interested in. Absolute pressure measures against a vacuum reference. This type of pressure gauge would measure the 2000 psi at the bottom of the sea.
See: http://www.dynisco.com/literature/Application%20Notes/Process/GageAbsPress.pdf
Bingo. The scale will read zero, because the pressure is from all around and even below.
I think we can take it for granted that we have some sort of sealed, waterproof scale here. I think you’re fighting the hypothetical. Then again, maybe not.
The OP specified the scale. It’s not some thought-experiment 2000-psi-rated thing. It’s this:
I’m picturing one of these: standard mechanical bathroom scale. It would work fine under water, and it would read zero.
It’s clear that any real-world bathroom scale will read zero at the bottom of the ocean.
But the OP also asked whether a scale reads the sum of the force on top and the force on the bottom. It’s a separate question, whose answer is No.
It wouldn’t work fine under water, in the sense of accurately measuring your weight. You are buoyant – if you stand on it under water, it won’t give a true reading.
So, what would the reading show if you placed something equal to your weight that wasn’t buoyant on it?
Not all people are, and it depends very much if you have air in your lungs or not.
I second that it would show the weight of the water column covering it. The depth meter I use while diving is a pressure sensitive plate on top of a spring that shows depth as a factor of external pressure. Scale it up a bit and make it square, and you have a bathroom scale.
