If the elevator is going at a constant speed, then the person's weight would not be any different than if it were standing still, no matter if the elevator was going straight up or diagonally.

To feel a difference in the person's weight, the elevator would have to be accelerating. So, if a person was in an elevator that was ACCELERATING upward, s/he would feel heavier during this time.

Suppose two elevators were accelerating at the same rate, that is, getting faster and faster each second by the same amount, but one was going directly vertically, 90 degrees to the flat ground, and the other was going up at an angle that was less than 90, say at an angle of 30 degrees up from the flat ground, and say that both had accelerations of 2 meters/second². The one in the vertical elevator would feel about 20% heavier than if she were not accelerating, and the one in the diagonal elevator would feel about 10% heavier than normal. I knew this because the vertical component contributes an amount in proportion to the sine of the angle, in this case 30 degrees. The sine of 30 is 0.5. I don't know if you've done this in math yet, so ask your teacher to explain it.

The reason for this is that you add the mass x acceleration to the weight of the person, which is mass x "g". g is the acceleration of free falling objects close to the surface of the earth, and it is about 10 meters/second².

If the elevator is going at an angle, then only the vertical component of the acceleration adds to the increase in weight. But, there's more: you asked about the total force on the person. Well, in the diagonally accelerating elevator there is also a HORIZONTAL component of force on the person, so he or she would feel pushed back toward the wall, like you feel pushed backwards in your seat when the car you're riding in accelerates forward. And that component is proportional to something called the cosine of the angle, in this case 30 degrees. The cosine of 30 is about .86, so for a total acceleration of 2 meters/second², this is about 1.7 times the mass of the person, or about 17 percent heavier.

So: for the vertical elevator, accelerating upward at 2 meters/second²,there is no sideways force, and the person feels about 20% heavier. For the diagonal elevator, the person feels about 10% heavier in the vertical direction, and there is a sideways force on her that is about 17% of her weight.

BUT - you have to remember that this is ONLY for accelerating elevators. If they're going at a constant velocity then there is NO extra force.

From classical physics, Force = mass x acceleration. So, for a person at rest, their weight is simply their mass times the acceleration due to gravity. Now, for both cases you described, their weight would still be exactly the same since the elevator in both cases is traveling at constant speed. If there is no acceleration, then there cannot be any "extra" force. Think about when you get on an elevator to go up. When the elevator first starts, you'll feel "heavy" because the elevator is accelerating. But if you were going up a long ways and the elevator speed became constant, you no longer feel the extra force, and if it's a smooth ride, you won't be able to tell if you're moving or stationary.