Translation:I know that.
I think it might be. I reported it and got the e-mail that my answer had been added.
Doesn't wakarimasu have more a sense of to understand than to know?
Yes, on its own; however, the progressive form, "わかっています" (note the "-te imasu") connotates a continued state of understanding, which is best translated as "know"
I've always understood わかります as being more polite than しります, particularly in the negative sense. Eg わかりません = I don't know (yet), しりません = I don't know (and don't want to know). I get the sense that しります or しっています have the meaning of 'I know that fact', whereas `わかります or わかっています have the meaning of 'I know and understand' (I know it well; I'm interested in it; it means something to me)
That's very interesting. I would have thought of to know as more of a single, discrete action than to understand.
I thought so too, as 知る means "to know". I would have thought the Japanese for "I already knew that" would have been それをもう知っている or something to that effect.
I can't help but hear this in a really petulant, defensive tone... but I imagine a native speaker wouldn't say it like that and also use ます.