I had a hard time understanding this but I've not yet finished book 2 (maybe 75% of the way through). Seems like Kaladin was constantly finding new spheres as opposed to just recharging what he had.
Spheres recharge when they are left out in a Highstorm. They pick up and store Stormlight from the storm. Since Highstorms occur every couple of days, it's not hard to recharge spheres, but Kaladin is a fairly active fellow, with not a lot of spheres, so it's not surprising he needs to scrounge Stormlight where he can.
Adding to this, towards the end of Words of Radiance...
...they are entering the period of the season called the Weeping, where Highstorms slow then stop altogether. This is what Dalinar's military plan is relying on, that the army can reach the Parshendi and end the war before the Highstorms resume, and not have his people exposed on the Shattered Plains with no shelter from the storms. So if you're in that portion of the plot, Kaladin is looking for more spheres because there's been nothing to recharge them lately, and he's not the only one doing so.
IIRC its stated in the first book that if you leave a dimmed sphere outside during one of the surge storms (or whatever they were called) it would brighten again
The bright spheres are the ones that have usable power in it so a sphere that has been left in a storm is recharged so to speak unless I am mis remembering