What sort of sources work on Skeptics Stack Exchange?
According to this FAQ answer:
References should have credibility in the domain (i.e. no encyclopedia, no source which may be biased, etc.) and should preferably be peer-reviewed literature.
Also do ALL sources have to be credible?
For example, there is evidence that may be weak by itself. However, combined with other strong evidence it qualifies.
Low-credibility sources may be down-voted. (Let's face it, even you shouldn't trust them.)
If you are synthesizing an answer from a number of low-credibility sources, you are probably veering into Original Research - find a credible source instead.
Should all the weak evidence be removed?
Weak evidence, by itself, isn't an answer. Using weak evidence, with strong caveats, to suggest where future research might lead us might be appropriate.
Say someone lists 10 sources, and one of the sources is a bit weak. Does that mean the whole answer is bad? My understanding is if I have 9 strong sources and 1 weak source, the strength of my answer should be 9.5, not 0.
Evidence doesn't add up like that. (Chat to a Bayesian statistician about how it might work.)
In theory, the extra reference shouldn't hurt your case, but in practice, I would probably drop the weak reference - why let it distract from your argument and have the comments fill with attacks on that one reference when you have nine good references to support it?
Is strong evidence the only criteria for "sources"?
Here are a stack of questions that address various issues with references that have been provided:
Can we add our own analysis on top of the sources?
Please avoid it. Sometimes people will add analysis to clarify an answer's context after they have answered the actual question (e.g. "No, the Prime Minster's claim is incorrect [reference], but I think that autocorrect might explain why they were wrong", and we let that by. But generally, Original Research is not permitted.
Does common knowledge need a source?
If it is at a level taught in High School, we generally don't ask for references. (e.g. if you said "Carbon dioxide is a greenhouse gas," we wouldn't ask for references.)
However, if it is the very core of the question being asked, it should be referenced. (i.e. if the question was "Is Carbon dioxide really a greenhouse gas?") an unreferenced answer just saying "Yes" wouldn't be acceptable.
Note: This is about common knowledge. Not about "common sense". "Common sense" is pretty much a term that celebrates human biases over evidence, and isn't well received here.