Your answer is right there in front of you, your jump is jerky but your fall isn't. What's the difference between the way you implement those two features?
TLDT: Your falling is implemented with an acceleration but your jumping is implemented by instantly setting the velocity. So come up with some
jump_acceleration and a
max_jump_speed (probably -8000 based on your code) and implement a process very similar to what you're doing with gravity except capping the max speed (which you probably want in the opposite direction for gravity as well, depending on how far the character can fall and how high your gravity is)