You're basically just modifying the weights you've loaded from the initial .h5 file during training, thus, you will end up with a file of same size but with different weights. The size of the file will change if you modify the construction of the network model in your code. Imagine a model having the weights
[0.1234567, 0.2345678, 0.3456789]
saved as an .h5 file. When you load this file together with the neural network model file (.json) and retrain it, it modifies the weights based on your training data. In our example, let's say the weights were modified into
[0.1212121, 0.2323321, 0.1221231]
When you save the modified weights into a new .h5 file, it will have the same size, just different values.