Watercolor paper comes in various weights and the lighter variants can buckle (also known as cockling) when they get wet. How can I prevent or reduce this from happening? Is there a preferred technique or should I just buy the really heavy paper?
To prevent the paper buckling/cockling you pre-stretch it, That is you wet the paper and tape it down to a rigid board with gum strip. I generally use a wooden drawing board that I made in work shop practice 50 odd years ago. Note masking tape does not work as well as gum-strip for this as it does not adhere very well to wet paper.
You paint onto the stretched paper and only cut it free from the gum-strip when finished.
Heavier paper (say 300+ grams per square meter) usually does not cockle when you paint on it using water colour technique (do not regard this as a challenge, I'm sure you could get it to cockle with a wet enough technique).
When paper gets wet, it expands. Apply wet watercolour to only part of the paper, and only part of the paper will expand, causing the paper to buckle. If there are no constraints on the paper, the paper will dry buckled.
(This effect will be less noticeable the thicker the paper is.)
Before you paint
You can purchase blocks of paper where every page is attached to the sides, and thus stretches the paper while it dries, causing it to dry pretty flat.
You can achieve the same effect (although less effective) by taping loose sheets to a board with masking tape.
Another method is to immerse the paper (should be at least about 180 g/m²) in water completely before painting. This way the paper expands uniformly in all directions and dries pretty flat as well.
After you paint
Sandwich your paper face down between two layers of cotton fabric and steam-iron your paper (in all directions). Put a board and some weights (heavy books) on to dry. If you look to frame your painting, you will probably want to do this step, regardless how flat the paper dried with the above methods.
At one time there was a mixture called sizing made from scrapings of still wet rabbit skins the inside of the skins.
You would wet the paper with water first then tape it down to a board with a heavy tape like duct tape then brush it down with sizing. Once the paper dries, brush it down with sizing again, allow it to dry, then size it one more time allowing it to fully dry.
You should be able to cut the paper then and be able to paint on it without fear of it buckling.