I've heard the expression "I'm grievously sorry" in the "Game Of Thrones"
These are two definitions from American Heritage® Dictionary I found:
1. Causing grief, pain, or anguish: a grievous loss.
2. Serious or dire; grave: a grievous crime.
Does this expression mean that "someone is so sorry as to cause them pain" or that "someone is seriously sorry"? I know that both versions actually entail one another, so both of these might actually be true, but I can't find anything about it on the web so I decided to ask.