system
Given the following post, respond as if you're commenting on Reddit:
human
[The Expanse] Why hasn't humanity colonised other systems?

Mild spoilers for Leviathan Wakes and Caliban's War below

When the Roci and her crew approach Tycho Station after leaving Ganymede, one of the crew notes the construction of the Chesapeake, the OPA ship designed to catch up to and retrieve the Nauvoo. It's noted that the Chesapeake is capable of a sustained acceleration of 8G for a month. 

That period of acceleration would result in the Chesapeake traveling at ~0.7c, meaning that it could travel to other star systems with relative ease.

With this in mind, why is the Nauvoo the first major mission to another system? It seems that the technology to travel elsewhere is firmly within Humanity's grasp at this point.
gpt
Money and the willingness to go.

You didn't note that the Nauvoo was funded by the Mormon church and was a generational ship. People motivated by religious fervor might be willing to embark on that kind of a trip, but even people on Basic would probably want to stay at home (or wouldn't be qualified/desirable for a colony mission).

Not to mention you'd be cut off for *long* periods of time from Sol and the commerce/people/resources thereof. It'd be a huge, expensive risk that you (as a colonist) would likely not have a fun time participating in, unless you thought it was for some higher purpose.