Yes, it means to shed tears. It is obviously used here in a figurative manner, a literary device known as personification , attributing human characteristics to non-human forms.
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ESLBeginnerThanks for telling me the word 'personification'; but I mean, if 'weep' already means 'shed tears', why would someone say 'weep tears'? here the word 'tears' is duplicated because 'weep' already equals to 'shed tears'?Good point! Perhaps for emphasis? Also, "wept tears of joy" sounds fine to me.