This site is a resource not only for you but for others. Part of what makes the site so useful is that the signal-to-noise ratio is high: there's a lot of useful information, and it's not cluttered up with other stuff.
So, the etiquette on Stack Exchange sites tends to be: Don't write "Thanks". Don't write "+1". Not even "+1 for the second sentence." Instead, thank the answerer by upvoting their answer, and accepting the best answer that most helped you. That's the most effective way you can thank them and help others.
It might seem polite to write "Thanks" for "I really liked your second sentence", but when you take into account that your remarks will be read by many other people other than the answerer and you are effectively wasting their time by cluttering up the page, arguably refraining from posting such comments is actually the more polite thing to do.