What happens as you pile mass into a planet is that the planet becomes dense, not large, and this is because of gravity.
Jupiter has more than twice the mass of Saturn, but is only moderately larger in diameter.
You can keep dumping mass into a planet, and it just won't get much bigger, until you have enough mass that fusion kicks off, and then suddenly the now-a-star inflates, because it becomes extremely hot and then you have something the size of the Sun.
It's more complexe than this. Yes Jupiter is twice as dense as Saturn, but so is Uranus, which is much smaller.
Also the main reason for why Jupiter is just moderately larger than Saturn is that, at equal density, mass goes as the cube of diameter. If Jupiter had a density as low as Saturn, its diameter would only be 26% higher than it is today, and just 50% bigger than Saturn despite being 3.3 times as heavy.
Do we even know what's inside the gas giants, how big is the rocky core inside (if any)? Having probes dive inside of the gas giants for exploration would be an awesome space mission!
The Galileo mission to Jupiter carried a probe which dived into the atmosphere: https://science.nasa.gov/mission/galileo-jupiter-atmospheric...