The Dropbox web interface is not super intuitive but there is a way to show the folder size, it's just a little hidden.
- login to your dropbox
https://www.dropbox.com/home
At the top click where it says Modified and in the drop down change it to Size
- After it's changed from Modified to Size click the check box next to the folder you're interested in.
- Now on the right hand side at the bottom should be a new link called Calculate Size
Note : if the folder is big it may take a while for it to calculate the size.