One reason why snickerdoodles may become puffy is too much flour. It's important to always use the spoon and scoop method when measuring dry ingredients. Use a spoon to fill a dry measuring cup with flour. Do not shake it or tap on the counter to pack it. Use a butter knife or something similar to level the flour that exceeds the top of the measuring cup. Packing flour into the cup or scooping it directly out of the container will cause it to be compacted and actually over-measure for your recipe affecting the final bake of your cookies.