Does the size of a bike tire matter when going up and down hills? I am doing science fair and my question is if the size matters when going up and down hill on a bike. I looked all over your site and I couldn't find anything about the size of a tire for going up and down a hill, but I did find something about the size of a tire help for going on flat ground but I'm not sure if the same will apply for going up and down hill. Sorry for the bother but it would really help me out if you could answer my question.
I assume you're testing a tyre's width, not its total radius because that would change the rim size. 
I'm also taking this as &quot;how to design a tyre test &quot; because otherwise you're asking for opinions, which would not be very Scientific, and would also be off-topic.
There's a lot of things to vary.  Good scientific tests try to fix all the variables except one, which may not be possible.
Assuming that adding weight makes a climb harder - that's easy to test by adding some non-functional weight, and timing it.
However testing if a wider tyre helps, will add weight as well, which we know from previous test will hinder the ride.  But how would you test if the wider tyre alone without the added weight is of benefit, or not.
To test &quot;Is X better than more/less X&quot;  will require you to isolate, or at least account for:

Weight, as already mentioned
rolling circumference  (A wider tyre has a subtle increase in the distance it rolls per revolution, which slightly changes the gearing)
tyre pressure (wider tyres have lower recommended pressures)
tyre rolling resistance (how much it deforms as you ride)
tyre grip
tyre wear
tyre construction (Ideally test a tyre that comes in multiple widths in the same model, and not test a commuter tyre against a race tyre)
road or off-road surface condition, dryness and grip and temperature
air pressure and temperature and humidity
wind speed and direction
rider' freshness, hydration, mood, enthusiasm, and total power output
aerodynamics of the rider and bike, and change.

So a well-designed experiment would see you testing one single change (tyre width)  with the same tube/bike/rider/course and to use a penalty weight in a fixed size container secured to the bike.
You might not think it significant,  but I changed from 47mm to 28mm tyres, which were 700g and 280g, so 800g saved between the two.
Also, you'd want to test a null case (where the grade is 0%)  as well as a range of uphill grades, and the same downhill grades.   Ideally you'd have a power meter to keep the rider's input power identical between test runs, and each run should be at least a minute long, with more adding to accuracy.   (though this depends on finding a consistent grade that is long enough)
Outstanding question:  Should you vary only one tyre, or do you change both?   When you finish your project, do please share the results here.