I am very embarrassed to cry in front of anyone apart from my husband and two grown sons. I don't think that crying is a form of weakness but it upsets other people and could make them feel awkward. Also, I am reserved by nature and feel that by crying I give too much of how I'm feeling away. There are people who do see any show of emotion as a potential weakness and look for a chink in your armour. To this end I would say, beware.
Crying at a sad or touching film is different to crying because of something that has happened in your life. It's a temporary thing but could be useful in examining which emotion is actually making you cry and which memories are stimulated,
A good cry is very healing so not something to be avoided whether it embarrasses us or not.