The Meaning Formula goes something like this:
The more responsibility = the more meaningful your life.
If you define a meaningful life as a life in which everything you do matters, it seems that this formula is correct.
The more responsibility you adopt, the more it matters what you do and don’t do. It becomes increasingly important what you do and how well you do it, because your choices have more consequences. Additionally, if you adopt more responsibility your choices affect the lives of an increasing number of people which makes what you do and don’t do even more important. But, responsibility also increases your ability to do good. The more responsibility you take, the more good you can do.
Take the example of someone who is nihilistic or hedonistic. They can “enjoy” more of life’s pleasures, but by doing that they also limit their ability to engage in meaningful activities that can improve the world. They avoid responsibility. As pleasures are always fleeting and don’t hold up against the suffering intrinsic to life, doing what is meaningful and not what is expedient is a lot more beneficial for everyone.
The more responsibility you have, the more your choices matter, the more meaningful your life.