It adds little to the meaning. I guess it adds a certain emphasis. "too scared of the height" is not actually wrong I suppose, but the usual idiomatic expression is "scared of heights".
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AnonymousWhat does "just" meanLiterally it means simply, merely, but knowing that alone doesn't capture the feel of it. just adds the speaker's attitude toward what he is saying. So I suppose you can say it is an intensifier, and as such, it is not necessary to the ov"just"here in this text?