If you want to make him respond with just a squeeze, every time you ride him, do it this way and never slacken off. Squeeze him to go forward, and if he doesn't respond, whip him with a crop straight away. If you ride him like this every time, he should start to learn that he needs to go faster when you squeeze him. This method will take some time, but your horse will eventually learn what's wrong and what's right. I did this the others day when I ride and within 10 mins he was responding really well, to the point that I was asking him to trot but he started to canter from a walk. (This horse is a highly trained horse who has got into bad habits so it didn't take as long. Don't be worried if your horse doesn't learn as quickly!) Hope this will help you 😀
Sorry if i understand your question wrong English is not my mother language: i think you mean he needs a lot of pressure to keep on walking / trotting and doesn't do any step on his own?
For solving this problem I would "educate" him like the professional dressage riders do to make their horse go forward without doing a lot of work.
It's about being very consequent:
when you kick him don't do it every stride kick him more than you would do usually ( surprise him with a little bit too much pressure) so that he does 2or 3 strides on his own because he is so confused why you used so much leg. and when he slows down kick again .. you educate him to do the work on his own instead of kicking every stride and teach him that you make all the work and he doesn't need to.
When you kick him and there is no response: immediately use the whip ( it needs to be immediately so that he understands that it has to do something with your leg)
you need to be very consequent with this. Leg - if no response - whip - leg if there is response release for 2-3 strides until he slows down and then again leg ... and over and over.
If you need to use your leg every stride because he is alredy so "numb" to your aids and he doesn't even walk one step without your leg. Try during trot: to not release the pressure for 2-3 strides in a row -use ur leg (maybe the spur) and just continuously stay there until there is a response. - sit deep in the saddle with a very steady leg.