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Correct me if I'm wrong, but isn't anything under .5 considered extremely weak correlation?

The short answer is, "no, but it depends." If sample size is large and the sample is representative of what it claims to show, .5 is very significant correlation.

The .3 correlation with a large sample size means something is happening. I agree with what Matt is saying: that content that gets +1s also gets links and mentions and everything else that Google might use to calculate rankings.

The pearson correlation, when squared, gives the % of variance (in the strict mathematical sense) that is explained by this variable alone.

So how much is 'weak' or not depends on the situation. If you have something that is influenced by multiple causes, then it is impossible to have any single high correlation. But any correlation, if statistically significant (i.e. highly unlikely to be caused by chance) can be important.

The question is, how much is an 'interesting' amount of the total variance, in the given situation.

(In the topic under discussion here, I have no idea.)

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