"I am very well, though."
Though must have caught your eye :) Anche se would be used as a conjunction. Though has that function as well, but here it is at the end of the sentence and does not have that role. Although or even though would be closer to the use of anche se. A few examples:
- I like insects even though I do not like spiders (Mi piacciono gli insetti anche se non mi piacciono i ragni)
- Although I eat candies, I do not eat chocolate (Anche se mangio le caramelle, non mangio il cioccolato)