I have been practicing with a lot of wedding cakes, but my layers are not nearly as thick. What do I need to do for this? Simply make more cake batter and cook longer, buy deeper pans, or use 3 layers per tier?

Thanks!

A standard wedding cake is 4" high. You can achieve this with 2-2" layers or 1-3" cake, torted and filled. This tutorial that I made is geared toward preventing bulging, but it shows you how to make perfect 2" layers. After I've torted both my 2" layers and filled them (4 layers cake, 3 layers filling), my cakes are about 4.5" high, but I enjoy the slight bit of extra height. http://tinyurl.com/pq9swv

This batter chart might be helpful:
http://www.wilton.com/cakes/making-cakes/baking-wedding-cake-2-inch-pans.cfm

Buy and use the "magic cake strips" to prevent waste from the humps. The pack of 4 strips is intended for the larger cake pans. You will have moister as well as evenly baked cakes.

Slightly off topic, but are wedding tiers ALL four inches tall? I've heard that the cake looks distorted when the 14" tier I the same thickness as the 6" tier. Is this true?

I have never heard or experienced that.