Pocket: more bag space

Each Pocket level adds +1 slot. The bag starts small (a three-slot maximum has been seen early on, rising to four after an upgrade). Buy Pocket when your trips keep ending before your machines are full.

Eyesight: see what is inside

An uncut rock shows the cores it might turn into. The in-game description, read out in the BemmyBlock video, says each Eyesight level rules out one wrong option, so with more levels you know more exactly what you will get before you cut.

That makes Eyesight the upgrade for finishing your Index: you can pick up only the rocks that hold a core you are missing. Three separate gameplay videos describe it this way. No source has shown that Eyesight changes the odds on a room panel.

Upgrade costs seen so far

UpgradeLevel shownEffectMoney cost
PocketLevel 4+1 slot$1M
EyesightLevel 4+1 sight$340K
Reported by cutarock.wiki from gameplay footage. It is not clear from the footage whether Level 4 is the current or the next level.

The Ultimate Boost Bundle (249 Robux) adds one permanent Sight level and one bag slot on top of the four 2x boosts. They are not sold separately; see gamepasses.

Pocket, Eyesight or a pickaxe?

Your bottleneckBuy
Cannot break the next doorA better pickaxe
Machines sit empty between tripsPocket
Missing cores in your IndexEyesight
Rocks waiting for a free machineMachine upgrades

Questions

What does Pocket do in Cut a Rock?

Each level adds one bag slot so you carry one more rock per trip.

What does Eyesight do?

Each level rules out one wrong option among the cores an uncut rock might give, so you can see what you will get before you cut. It is most useful for completing the Index.