Why used "on" here?

This vignette study examines the effects of group-centric motivation and a shared ingroup on weakness perceptions.

Quote:

This vignette study examines the effects of group-centric motivation and a shared ingroup on weakness perceptions.

To paraphrase: This study examines the effect of X and Y on Z.

http://idioms.thefreedictionary.com/have+an+effect+on

That's pretty close, yes. They share information and also values regarding what constitutes weakness.

The experiment was testing only those two variables, so they would be limited to those two.

Sociological stigma research may contribute to current knowledge by acknowledging the
importance of the norm context in which stigma occurs (Phelan et al. 2008). Examples of the
U.S. military's cultural norms include group coheson and individual strength in coping with
trauma (Kirke 2010; McFarling et al. 2011). While these norms help to maintain a unified
fighting force, their enforcement may foster divisions between individuals seen as fit for duty
and individuals seen as too weak to handle the stressors of military service.

This study examined the potential for three factors to mitigate stereotyping of treatment seekers .
I tested the effects of two experimental manipulations on weakness perceptions in the U.S.

Something like "Kirke 2010; McFarling et al. 2011" would be a note at the bottom of a site or at the end of a chapter.
It means, the author had quoted from several publications of "Kirke" and "McFarling et. al.", refers here to those from those years.
The excat source would be at end of the book - the biography would show full title, publisher/location and year where the source was published. With these data, you can find them easily.