I too hate heights, or rather I hate exposure to heights which is a different thing I believe. Walking along mountain paths in the Alps I can feel my anxiety levels creeping up the narrower the path becomes. Quite irrational as their is virtually no chance of falling from the path over the side.
I have no problem at all when flying, although I once tried a tandom paraglide flight in Switzerland and suffered greatly. The strange feeling of being suspended way infront of the instructor in what felt like a very slack harness with several thousand feet of valley floor beneath my feet certainly made me feel very exposed. When he handed me control of the wing I felt much better, in fact I came to quite enjoy the experience! I might even do a course one day!