The very short answer is that gas pressure is mostly proportional to the amount of particles per volume.
So a balloon filled with helium has X particles per cubic cm, while the air around it has the same amount (instead of getting crushed). But because helium is a lot lighter per particle than standard air, this makes the balloon lighter than air, and like trying to push an air-filled balloon underwater, this helium-filled balloon floats to the higher layers of air, until other smaller forces also start to matter and the balance is restored.
So a "vacuum-filled" balloon has nothing to give counter-pressure, but a balloon filled with helium definitely does.
Close, but now you come into contact with the atmosphere not actually being the same density (in weight/volume as well as in particles/volume) throughout, but instead gets thinner as you get away from the earth.
For simplicity, assume space is actually empty, and the atmosphere gets thinner linearly up until x kilometers above sea level it's completely empty. Then the density will also decrease with height, and the helium balloon will eventually find a spot that matches its density, and stop there.
Again there's so much more to it but as a simplified model this works 😅
Rockets mostly need to fight speed (of the earth revolving around the sun), and indeed in our atmosphere speed means friction, but in space rockets still need a lot of propellant to change their trajectory. As always there's a relevant xkcd: https://what-if.xkcd.com/58/