should I send a rather weak SAT II?

I got a 690 on the SAT II Latin, should I send this score, or will it hurt my admission chance?

UMich does not require SAT2 but they would consider it if it is a great score for the good of the student. A weak score would not help or hurt and you may save the money if you are sending in ACT score. There is no reason to hide it though.

so would this be considered a weak score? It’s well above average (while a 690 in math II would be well below average)

690 is not a weak score but it would have no effect on your admission. It is at about the 70th percentile. Note that the ACT/SAT admission score range are well above the 90th percentile.

What are you applying for? LSA or…?

Yes, LSA