Why do helium balloons expand in volume as they go higher? I realize as balloons go higher, the atmospheric pressure decreases, doing less to counteract the force of the gas particles pushing against the inner walls of the balloon. But at the same time, doesn't the outside temperature decrease, causing the gas particles in the balloon to lose energy and have less impactful collisions and a lower velocity? Is the reason why the volume nonetheless increases because the pressure outside decreases faster than the temperature? Or am I overthinking this?
I didn't know that balloons expanded during the fly because of thermodynamics, and I didn't know how high they can fly, but a rapid search tells that a partially unfilled regular balloon can fly until an altitude of around $\pu{25 km}$.

Now, $\pu{25 km}$ means that it reaches the first part of the stratosphere, with temperatures of $\pu{-60 ^\circ C}$, that gradually increase until $\pu{0 ^\circ C}$ at $\pu{50 km}$.
As for the pressure, it goes from around $\pu{40 mmHg}$ to $&lt;\pu{1 mmHg}$ in the range $25\text{–}\pu{50 km}$.

If you try a $pV=nRT$ calculation on these data, you see that the gas is already at around 10 times its initial volume with $\pu{40 mmHg}$ pressure and a $\pu{213 K}$ temperature, and that at the $\pu{50 km}$ point the volume is increased 700 times!

Also: while the trend of the pressure is quite logical, that of temperature is caused by complex interations (eg: sun rays that heat particles). You can find this image quite interesting: