Common fashion advice states that black is a slimming color, when one wears it, they appear slimmer looking. Is there any evidence this effect exists? What would cause it?
Yes, to some extent
The way our eyes detect bulges on a body is largely due to lighting effects. We can see that someone has a bulging belly because lighting cues give away the contours. The same is true of wrinkes - we see them because of lighting patterns. Wearing black reduces those lighting cues, and the bulging belly isn't as obvious to the eye; nor are the wrinkles. It works for other bulges too - I've read stories from actresses saying costume designers made them pad their breasts in scenes where they were going to be wearing black or in dim lighting.
Another point is that our eyes really do see dark objects as (slightly) smaller. It's an optical illusion; that's exactly what 'looking thinner' is all about.
This effect is obviously limited. If you are looking at someone in silhouette, side on, wearing black will make no difference to how fat they look. And black can't work miracles. And black won't fool someone making a careful examination of you. But yes, black can make you seem a little thinner under some circumstances to the casual observer.
References for this are hard to come by (since scientific journals don't usually include a fashion column). Here is a really good one looking at the science behind fashion in general. It includes a reference to the optical illusion that underlies all this. Here is another more explanatory article.