The phrase I'm out of energy means: I'm tired, and not energetic.
The phrase is used in various contexts, and could be used to describe mental energy or physical energy.
For example, a basketball player might be out of energy, and ask for a sub to come into the game, so he can rest on the bench.
Or, on Friday afternoon after a hard week at work, a teacher may be out of energy. This means – those essays her students just handed in? She will carry them home, and grade them on Saturday after a good night's rest. She doesn't have enough mental alertness to deal with them right now.
I'd also say that the phrase is somewhat figurative. Many times, people who say they are "out of energy," actually have could be more energetic, but they are just wanting to relax. For example, the basketball player is probably not on the verge of collapsing, but he probably won't play very good defense. The teacher probably could grade the papers if she really needed to, but it's not an ideal time to do so.
The expression could also be used to describe teams, too, and not just individuals:
After the German team scored their first two goals, the Brazilian team seemed to lose their energy.
This doesn't necessarily mean that the Brazilian team looked tired, but it could also mean that they looked discouraged, and played with no heart.
...does more so in this case means that he worked even harder than me?
Yes, but the word probably is important here. The speaker isn't certain that the other person works harder. The speaker is guessing about that. However, the speaker is certain that at least they worked equally hard.
This kind of sentence might be used when another coworker received a promotion and you didn't.
"I thought I deserved the promotion more than him. It wasn't as if he didn't work just as hard as I did --- more so, probably. However, many customers complained about his rudeness and he was often late to work."
Best Answer
This is an idiom for a disastrous loss or collapse. As the American Heritage Idioms Dictionary has it (via Reference.com):
A very similar expression is for something to fall through the floor, similarly indicating a breach of what was previously thought to be the worst something could be.
The quoted text, therefore, is alluding to a dramatic decline in the condition of the European economy in the 14th century. Coming as it did indicates that the timing of it is significant— in other words, the closing of Europe's overland trade routes with Asia occurring at the same time the European economy was in poor condition made the pursuit of seaborne trade all the more important.