I go to a lot of funerals. I don't think it would be strange to attend the funeral of someone you did not personally know or if you cried. Some people just cry easier than others, so I don't think it would be that unusual. I have even seen people that are part of organizations that are based on going to funerals cry at them.
At the same time, I don't think that you need to go to the funeral to be supportive.
At the same time, I don't think that you need to go to the funeral to be supportive.