My maker does not keep me, my buyer does not use me, and my user does not see me. What am I?

I'm by design a sign of turbulence, though often symmetrical. I raise your arms in patterns, yet am found in the mathematical.

I determine the error as you fire a bow. Very much a requirement, so please take it slow. The shots are precise, but may not have me. Don't make that mistake, I am ...

I grow when you take, I shrink when you give. I thrive in loss, yet live to forgive. No weight I carry, yet heavy I stay. What am I?

I am many things with many tasks, I swim with sharks and grade the flasks I summit mountains, I model towns, I measure disasters that bring them down. I rise and fall in musical calls, and sometimes ponder the weight of it all.