Tears are important to God. He made us and our emotions in such a way that sometimes tears form as evidence of those emotions and they also act as a healing agent. Tears are not always because of pain or sadness, they can also be because of joy! In any case, we do not need to be ashamed of them. Never believe it when someone says that they are a sign of weakness. Don't forget that Jesus also cried and shed tears. Things that touch your heart and move your soul are capable of forming your tears.
A verse in Psalms has for a long time been a precious one to me for it shows that the Lord knows about and cares for whatever we're going through that is causing our tears. Psalm 58:6 says "...put Thou my tears into Thy bottle: are they not in Thy book?" I like the thought that He cares SO much for us that each tear is precious enough to store in a bottle that He has just for that purpose. Not only that, but it seems that maybe He writes about those tears in a book! How wonderful is that?!