[SPOILERS] The Tree

[13ventrm]

So I'm curious as to what eating the fruit actually does for future playthroughs. I refused it because my run was all good so I didn't see the point in being able to go back at that stage. Plus it certainly didn't seem to help Hunt be any more successful in his endeavors and it felt implied he got stuck in a time loop doomed to failure because of it? Does it like grant new options, curse some, keep the game looping, etc?

[FlyingAllNight]

Same spot as you. Refused but kept the tree and sailed it home.

[Agentw22]

If you eat the fruit, Your save tree will be fully unlocked and you can go back in time to change your decisions. It creates new branches at your will. This way the game moves into a kind of new direction and the saving tree makes sense now, before it I thought it was useless.

[Polaris™]

Like @Agentw22 said, the fruit allows you to return to all individual weeks that were previously locked, and it also provides your character with the memories from all the endings you have unlocked for replay attempts.

As far as I understand this is necessary for a few achievements as well - I'm currently trying to get "Worth his Salt" but I'm still testing.