Google’s John Mueller said in a video hangout 22 minutes and 21 seconds in that there is no magical SEO advantage when switching from HTTP to HTTPS.
But didn’t Google tell us that HTTPS is a ranking signal? Yes, but only a “very lightweight signal” but that may increase over time. It hasn’t yet.
Jennifer Slegg first covered it and transcribed it:
Here is the video:
My thought, if you know what you are doing, do the switch. It can only benefit you if you do it right and in the long run, Google will tweak the signal and give more weight to it.
Forum discussion at WebmasterWorld.