I object to you having a girlfriend. vs I object you to having a girlfriend.

[Cerberus™]

I'll tell you something of their etymology. Both come from Latin iaceo, meaning "to throw". Both are passive past participles. Subiectus means "thrown under [something]" and obiectus means "thrown in the way of [something]". Their meaning is not intrinsically very different.

In philosophy:
- The subject has come to mean the agent of action or perception, looking from the "I" perspective or active perspective.
- The object is the thing that is exposed to an action or perception, as in the "other" perspective or passive perspective.

In linguistics:
- The "subject" of a sentence is the thing or person that does the action of the main verb. It determines the form of the verb: in "he hits me", the s in "hits" is added because the subject is in the third person singular.
- The "object" is the thing or person that the action is performed on, that experiences the effects of the action. In "he hits me" the object is "me" and it has no effect on the form of the finite verb.
They were already used this way by Roman grammarians.

As you can see, the "subject" has changed from a passive role in "thrown under" to an active role in philosophy and linguistics. In "to be subject to something", however, this passive role has been retained.