Most horses don't do more than canter over things that small, especially when they get really accustomed to jumping, I don't think I've ever watched a cross rail class and thought, wow that horse really jumps in good form, maybe a small pony though. At that level the judges aren't really looking for that anyway, just a calm consistent horse that safely is doing or in some cases, learning how to do a course. BUT, part of your problem is the fact that your walking over them, your kinda giving him the idea to walk over them, if you were trotting them he might react differently. I don't think walking him over them is a bad thing, probably a good way to introduce jumping where your main goal is to teach the horse to go over the fence. When he is more confident you can trot and canter fences of the say size and he might actually start jumping a little more. When the fences get bigger you will see him make an improvement, or maybe when he taps a rail for the first time he might actually think of picking up his legs. If you still aren't statisfied with his effort, gymnastics that include a series of bounces or one strides can get a horse to really jump a smaller fence. But have someone help you set that up right if you haven't set one before and make sure he is confident trotting and cantering single fences and lines before trying a gymnastic.
Troubled TB ~"A thorn by any other name will prick just as deep." @-'--,---