I remember learning that the reason for the rule that a non obligated person cannot do a mitzvah on behalf of an obligated person is because it's more difficult for the obligated person. What is the source for this?
The source that someone cannot do a mitzvah for someone who is not obligated is (very timeously!) a mishna in Rosh haShana 29a (or 3:8)
Anyone who is not obligated in something, cannot fulfill the obligation for others.
I am not aware of a source connecting this to the source in Avodah Zara which @Shmuel linked to, that it is considered greater to do a mitzvah if one is obligated.
In other words, the connection is false. (However, I would be happy to hear of a source connecting them if someone knows of one.)