The replacement of the neuter
In the third person neuter two changes happened. First a phonological change started in the twelfth century when the initial /h/ started to decline. Instead of /hit/ only the form /it/ was used. In the sixteenth century the /hit/-form could still be found, but mostly in spoken English. By the end of the century the form had completely disappeared in written English. Still today the form including an /h/ can be found. It is spoken in some dialects in Lowland Scotland and in the south of the US.
Where does the dropping of the /h/ comes from?
/It/ occurred for the first time in the late sixteenth century and was first mentioned by the grammarian Butler. The origin might be the addition of the genitival {-s} to the base of {it}, which is {its}.
The developing use of /it/
Even in the Mid seventeenth century /it/ was not the commonly used form in written English. It was ‘colloquial’ and not suitable for the high style. Shakespeare mostly uses his and only sometimes uses an “archaic zero-genitive” (Lass 1999: 148) it. In Hamlet I he uses this special zero-genitive: “It lifted up it head.”