Hi All, new here, but I have been re-reading these books for quite a while trying to squeeze all I could from them awaiting SA3.
As to Lightweavers, I think that there are two that we "Know" have cryptic spren, one is in denial/early-proto-stage (the King) and of course Shallan. There are two other good candidates, Kaladin's brother Tien, and of course Gaz.
Gaz's eye whacky theory:
We see Gaz glance away several times (once Kaladin mentally comments "what is he looking at? Did something move in the shadows?") And Once Shallan thinks he is turning to Spit (As he does seem to spit often and it might have been that), or he keeps seeing things out of the corner of his eye, which brings up the question, "How exactly did Gaz lose his eye?" was it in combat or did he remove it himself, or was it removed as part of a "repayment of debts incentive". At one point he lists other body parts he would have rather lost, but at no point does he make it seem that he felt he had a choice in the matter, and if it was self mutilation trying to rid himself of seeing the cryptic spren (perhaps always out of the corner of that eye?) it obviously wouldn't work, and thus he would lament the loss of the eye.
Tien Lightweaver theory (others have touched on this but the evidence adds up:
Tien has a notable memory, he remembers where he finds every rock. Tien is artistic, fabulous sculpter. Tien transforms Kal, every weeping removing his depression and most importantly, he transforms Kal into an excellent spearman as he knew that is what Kaladin wanted to be. When Kaladin first fights the the farmboy Jost, Kal gets suddenly and swiftly trampled, Tien was not there at the time, Kal gets up grabs the staff again and this time he feels that "Something changed in that moment", but after a few good strikes Kaladin cannot deliver a "face Smashing" blow to Josh and Josh counters before Kaladin can speak. So Kaladin hits the ground. Everyone leaves, except the one person Kaladin didn't know had arrived... Tien, and he says "How long have you been there?" This is Brandon's way of saying that the time Tien arrived is important. That something changed when Tien Arrived... Kaladin also thinks about how Shallan and Tien both brought light to their families.
enough blathering on my part. I looked through the forums so I wouldn't be too repeaty but I probably failed.