This "le" refers to "your son". It is an indirect object pronoun. Although it is clear in the sentence who the bottle is given to with "a tu hijo", sometimes we make it even clearer by adding "le/les" (to him/her/them).
There is a lesson coming up soon (for a higher level, though) about this. I hope this is clear for you now.
Hola D and Connor
The use of "le" or "les" in these sentences are optional. Here is a lesson about the repetition of indirect object pronouns. Have a look here.
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