By what right did Robert dispossess Stannis of his rightful inheritance as Lord Paramount of the Stormlands? Having read that, I’m surprised Stannis wasn’t MORE bitter towards Robert..

That’s stating things a bit too Stannishly. To begin with, Robert was the Lord Paramount of the Stormlands and could have given it to whoever he wanted – indeed, by rights it should have passed to one of his sons rather than his brothers. 

As GRRM puts it, Robert was known for “careless” generosity.