Most people likely have no idea that the State Farm jingle is actually just part of an entire song.
It was written long ago by a young Barry Manilow; yes the same creepy lounge singer you're thinking of.
Manilow wrote advertising jingles prior to becoming a successful recording artist. He also wrote the Band-Aid jingle.
Anyway, Weezer got their "Memories" tour from a while back sponsored by State Farm and conversely agreed to record this tune at a later date.
It's interesting because despite being about as commercial a song as there can be, it's as vintage-sounding a Weezer recording as has been released in the last ten years.
As drummer Pat Wilson said on the All Things Weezer message boards this week,
It's kind of good because =w= sounds good when we play in a room together at the same time with Rivers on gtr and me on drums. That took us about 45 minutes vs 12+ months for Raditude. This is why I'm in semi facepalm constantly!
Interestingly candid, but far from shocking observations on the dysfunctional nature of this band.