I prefer the same, but both are in use. The google results are statistically even, and if I do a COCA (a more reputable corpus) search, I get: 'at' - 316 'by' - 405
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Hmmm... Can't you be scared at the sight of something? I'm not an expert, but it seems like these things that prefer a noun clause or a sentence. I'm scared of you and I'm scared at the sight of you. What does everyone think?