If you are leaving to get a better salary, you can get a better deal from your current employer if you have an offer letter in hand. If you tell your boss first, you might be settling for less.
Something had to have pushed you to do all that work to find a new position; are a few thousand more a year going to fix it?
Never mind you'll forever be marked as the "one who will leave".
I could be alone here, but I never stop looking at job postings. If I ever see something more interesting than my current job, why not explore it. Chances are you would miss the most interesting opportunities if you weren't looking 90% of the time. The best time to search for jobs and interview is when you already have a comfortable job. Then your desperation doesn't force you to take something you don't love.
I like my job, but that doesn't stop me keeping an eye out for something better.