I think it can be measured. The sorrow you may feel about losing a friend could not be compared with the sorrow of a mother or father losing their child in a terrible accident or witnessing their own child's murder as an example. Every person feels and handles the sorrow differently but I do believe there are different types of sorrow.
You do not have to be a horrible parent. You could just be the kind of parent that did not show much interest or never talked with the child, maybe always working or off on trips, etc. Whereas the friend may be there for the needs of the individual and in a way acted as the support the child never had which the parent should have provided. Thus the question is... how do you measure that sorrow when the friend departs?
Is sorrow measurable?
I feel sad when I see a person have anguish over the death of a loved one. I also feel sorrow when a bird flies in front of my moving car, and gets stuck in my radiator.
Do I feel sorry for the bird? The angst at having been the protagonist of death affects me, but I worry more for the state of my radiator.
I fell out of love, once, and experienced the pain of loss. Was this sorrow, or just the missing of what was?
I can honestly say, the loss of love was my most anguished moment. I even cried for a while.
Time has a way of healing, but the immediate time after anguished moments are poignant for two reasons; 1) it teaches us Life lessons, and 2) It teaches us about our humanity.
The death of a loved one, the death of a stranger, the death of an animal.... this is part of the circle of Life. As such, we know it can happen, and we have inbuilt defense mechanisms to get us through our sorrow.
Sorrow is just one emotion. When sorrow departs, we are left with memories, and hopefully, they can make you smile.
Now, this next premise might make you wince, but I hope you read it with an open mind. Emotion has no place within the being of a philosopher! It is not a philosophers task to ask why an individual has particular feelings, nor to which degree those feelings delve. Such questions can never be answered, because they are asked of individuals. Philosophy does not answer to individuals. It asks wider questions.... matters that matter to humanity.
So, is sorrow measurable? It is measurable only to the experiences of the individual.
In other words, the question can only be answered by the questioner.
For me, sorrow is sorrow. Laughter is good. Anger is a waste of energy. And every emotion has a reason.