I think he cried because he is finally able to say it out loud without hiding it. He has been keeping it all in for 22+ years so now that his grandpa is okay with it, he is finally accepting this side of himself without feeling guilty 
Comment by Ko Ya on Here U Are - Vol.1 Chapter 132
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@Ko Ya I think yuan also knows that he likes him but he can't reciprocate those feelings so all he can do is just hold his hand