First thing I noticed is that your stance is quite 'frozen' - you pop up but then it seems like you are really afraid of falling so just stand very very still and dont move anything. So you will need to learn to loosen up. This starts with your head - watch the videos and see where your eyes are looking. Which is down at the nose of the board. You need to look where you are going, you never need to look at the nose of your board. So head up and that puts the weight more centred over the board (as old man says) for a start (your head is heavy, if your head is leaning forward and down then the rest of your body has to stick out to balance it). It will also twist your shoulders to be a bit more front on (good). Then you need to loosen up the knees and hips and let them move about a bit and be a bit lighter on your feet.
But just looking up will help an awful lot and is the place to start (it will also help you catch waves in the first place, as looking up helps you figure out where to go, avoid other surfers, balance your board better etc)
edit: one of our regular, waikikichan, has a blog that covers this - look here
http://alohaki.jugem.jp/?month=201611 and scroll down to the third entry 'Look Down-Go Down. Look Up-Stay Up'
Dont worry about it too much, looking down is a pretty common beginner level thing. But you do need to fix it.
Hope that helps
Might be worth reading through these two threads as some similar issues/points re stance and hips etc (you arent entirely the same but there might be some useful tips)
viewtopic.php?f=9&t=33343viewtopic.php?f=9&t=33348