"As much as" at the beginning of a sentence is usually a way to soften some bad news: As much as I respect you, I do not want to date you. As much as I want to help you, I have no money. As much as he trusts you, he is unable to make the deal. Yes, it is almost the same as using "though", but "as much as" gives a softer and gentler introduction to negative information or bad news.

As much as= no matter how much no matter how much I hate to do it,I must stay home and study tonight.. :)