It mentioned that during "the weeping" that Kaladin would get depressed and feel weak. During the weeping there would be no storms. So it seemed like he had this connection with storm light his entire life.
Like I said, there's been some debate (largely over this very quote), but seeing how we have WoB that Investiture on Roshar is not passed down genetically, but is instead gained through actions, we think that it must be spren bonds that allow people to use surgebinding. Most think think that this quote means that Kaladin suffers from some sort of Seasonal Affective Disorder that centers around the Weeping.
If Investiture is gained through actions, and since Szyth doesn't have an Honor spren, doesn't that indicate that there is some other act that made Kaladin a windrunner? Just a thought, I would be more willing to believe that it is dedication to a cause that turns one into a windrunner. Kaladin with his urge to defend and Szyth his dedication to being truthless. Or perhaps it is simply suffering such as snaping in mistborn... but to assume it is the Honor spren bond means that either Szyth doesn't have that bond and gained his ability a second way or that we just don't ever see his spren... unlikely I should think.
Szeth is a bit of a special case. His powers are a direct consequence of weilding an Honourblade. (Check out the Eshonai Interlude over on Tor for the quote.)
Normal Knights Radiant gain Surgebinding through a spren that has bonded to them because of their actions. Honourblades seem to automatically hardwire Surgebinding into the Spiritweb of the person currently posessing it.
There's still lots of discussion about what exactly is needed to form a Nahel Bond, but most assume that it requires a "broken soul" (like Snapping in Mistborn) as well as actions in line with a Spren's Intent.
Considering the fact that we can assume Normal men could become Radiant, mainly based on one of Dalinar's dreams in which a Radiant invites him(the person he is seen as in the vision) to go to Urithirua, it's safe to say that Kalidin got his powers from Syl.
(Spoiler) Syl picked Kaladin, it can be inferred from the second book. It is the way Kaladin's honor is his way of life, since the Cognitive World is made up of ideas, Kaladin probably attracted Syl who is an honor spren.
Syl picked Kaladin she had been watching him for a long time before revealing herself to him... She may have picked him at birth for all we know, but he didn't start to attain his Windrunner abilities until he started to adhere to the Ideals of the order.
(Spoiler) that doesnt explain Dalinar though, who realises just prior to bonding with the Stormfather (how the hell did that happen btw, as the Stormfather is a Herald...) that he has been using Stormlight during his career without realising
Dalinar had been bonded to the Stormfather (who's a very large Splinter by the way, not a Herald) for years before he spoke the Second Ideal, the same way Kal was using Stormlight unconsiously for a very long time prior to the Battle of the Tower.
126.96.36.199 wrote: If Investiture is gained through actions, and since Szyth doesn't have an Honor spren, doesn't that indicate that there is some other act that made Kaladin a windrunner? Just a thought, I would be more willing to believe that it is dedication to a cause that turns one into a windrunner. Kaladin with his urge to defend and Szyth his dedication to being truthless. Or perhaps it is simply suffering such as snaping in mistborn... but to assume it is the Honor spren bond means that either Szyth doesn't have that bond and gained his ability a second way or that we just don't ever see his spren... unlikely I should think.
Major Spoiler Alert!!!
Szeth got his abilities as a Winrunner from the Honorblade (he has no spren). It's the same concept as the Heralds' abilities, and it appears he has Jezrien's Honorblade.
Wait... I always thought that Stormfather was one of what I consider to be father-spren. They are the protectors and souls (if you will) of various cognitive ideas. The Stormfather is of wind, rain, and other sky elements; the Night Watcher of hope, dreams, and maybe pain; Kalek (don't ask; the name feels right) of earth, rock, and other ground elements; Almighty was of honor, strength, and nobility; Cultivation of all things involving life; and Odium (Rayse) of death, destruction, and malice. There are ten other father-spren, as seen in the death rattle "Three of sixteen ruled, but now the Broken One reigns."
I don't think it's necessarily a broken mind that attracts Nahel bond-spren. I think it is the person's character and true self; despite Kaladin's mistakes and the fact that he ___(you'll see in Words of Radiance) her, Syl trusts him wholeheartedly and helps him to find himself again. The only reason he noticed Syl when he was destitute is because he was completely bored out of his mind, had failed too many times to be happy, and let a "windspren" annoy him.
Odium, Cultivation, Honour (The Almighty) and the other sixteen Shards of Adonalsium (Endowment, Dominion, Preservation, Devotion, Ruin, etc.) are not spren. They are... Relatives, one could say. The Stormfather (a Splinter of Honour) and the Nightwatcher (a Splinter of Cultivation) are spren, albiet much greater spren than Honourspren, Cryptics, Highspren and the like (which are far more powerful than things like firespren, passionspren, etc.). All spren are Splinters of Odium, Honour or Cultivation. If you want to know some more, look up Shards and Splinters on the Coppermind.
A broken soul (not a broken mind) is something that is integral to all magic in the Cosmere. Actions and character attract Nahel spren, but without a broken soul, a bond cannot form, as there is no room for the Investiture. You won't be able to find this on the Coppermind though. If you want to find out more about how exactly this works, there's several good theories on the 17th Shard about it.