The ability description states (emphasis mine):
The slayer then gains a +1 bonus on Bluff, Knowledge, Perception, Sense Motive, and Survival checks attempted against that opponent, and a +1 bonus on weapon attack and damage rolls against it.
Some people I asked tried to say that the bonus does not apply on sneak attack cause it says "On weapon attack and damage rolls" As I see it, it's unclear if "damage rolls" is tied to "weapon", but even if it is, your sneak attack is a result of your weapon hitting a targets vital spot. So that extra damage comes from your own attack/weapon. Additionally the Sneak Attack is not a "fixed" number, like Str bonus mod, it's a damage roll/you throw dice and the part where the ability says that it applies on damage rolls fits.
So I would think that a lvl 20 slayer doing a sneak attack/performing a sneak attack with his weapon, by flanking/catching the enemy flat footed doing 6d6 sneak attack, on every dice of those 6 dices rolled is applied +5 from studied target.
Does anybody know/have any source that states/clarifies that the studied target ability does not apply on the sneak attack dice rolls as well? Or can someone who is able to contact the creators of pathfinder to illuminate us/me, about it?