If I build an hybrid app with Apache Cordova, how much overhead will be added to my app? I mean, how many MB will be added to my app package?
I'm concerned about the final size of my app
It depends on what you include in your project. In cordova you have plugins which will increase the size of the output, also you have some ui frameworks such as ionic or jquery-mobile or onsen-ui they will increase the file size too; java scripts, images, ... also will affect on your output size.
But the size of a simple Hello World application without any additional library in cordova is about 2Mb (which is greater than building native app with java)