The circle pad has nothing to do with background collision or gravity. It is just an input. If you want circle pad input use something like:
STICK OUT SX#, SY#. That gives you two floating numbers letting you know the direction the circle pad is pointed. The Y value is sign flipped from what you want so multiply it by -1. You will want to include a "dead" zone in the center you treat as no input to prevent noise. Long story short, unless this is a top down game where you move a full tile with every step, background collision is complicated. There isn't an easy fix. You need to make a physics simulation of some sort to get things working right. If you want sub tile accuracy that is even more complicated. Getting a nice arc for jumping is again physics. There is an article on time based movement on this site. Go find it and read it. It is good stuff. For proper physics you need to know how much time you are simulating. Anyway, for jumping you give your player a large velocity in the negative Y direction. The velocity says how many meters per second the player moves (you will need to map meters to pixels). So if they are moving up at 10 meters per second and a game meter is 8 pixels, then in a sixtieth of a second the player moves 1.33 pixels up. Gravity on Earth is ~9.8 meters per second squared. So when falling you fall toward Earth faster and faster gaining 9.8 meters a second additional velocity every second. In our example this adds about 0.1633 meters/second to the player's velocity toward the Earth (don't forget to account for terminal velocity). So the player starts out jumping up quickly, but gravity eventually zeros out their upward speed and they fall to the ground at a constantly increasing speed. I do have a smallish game with some Super Mario style physics. Can you try reading the code for Find the Exit http://smilebasicsource.com/page?pid=820 Key K2KYJCS I tried to keep the code readable and some of the physics are a bit bad but it should be some good example code. When you are finished feel free to post questions.