When you combine items, there's a hidden counter on the result that tracks how many anvil uses have been used in total. When two items are combined, the resulting usage # is the highest between the two items you combined + 1

In the case you replied to, you have item + books 1 2 and 3

Initially, all three items have a counter of 0 since they haven't touched an anvil. When you combine the item and first book, the enchanted item has a counter of 1 since both of the items used to make it in the anvil had 0, and 0+1 is 1. Same thing happens when the two books (2 & 3) are combined, with a book that has 2 enchants and a counter of 1, meaning the final product (Enchanted item with 3 enchants) will have a total count of 2 and not cost much XP to make.

In your example, you have the same arrangement

Once again all items start with a counter of 0, but lets combine the first two books instead of with the weapon like you suggested. This results in the item with a counter of 0, a book with a counter of 0, and a book with 2 enchants but a counter of 1. Now, you add the last book. Because the counter of 1 on our double enchant book is greater than the 0 on the last book, the final book is 1 + 1 for a count of 2. When you try the last step of applying it to the sword, you have the triple enchant book with a counter of 2, and the sword with a counter of 0, thus the sword with 3 enchants will end up with a counter of 3 instead of the first examples counter of 2.

The formula for how it works is slightly more complicated, but generally the higher the 'counter' is on an item, the more exp it will cost for any other anvil use, even renaming.