Make sure it ISN'T as Mike suggested. That tilting the outboard may be causing fuel to exit a vent. There are several vents in these carburetors.
When seeking the source of ANY liquid leak, always look ABOVE where the liquid is visible and see if you can discern a "trail" coming from someplace else. I would use a small dental mirror and a good flashlight to eliminate all other possible leak points before coming to a final conclusion. In my youth I had to "live" this lesson a few times when learning to work on 18 wheelers.
Is it an easy job to re-seal the float bowl? That is relative. I would say YES, others might say NO. It just depends on how mechanically inclined you are with disassembling things and then reassembling them. Because, that's basically what you are looking at, IF it is the float chamber seal. Fairly straightforward as my old boss used to say.
But, it doesn't sound to me as you you are very confident about working on your outboard so, you may need some help.
If you do decide to give it a try, I'm pretty sure it is easier to take ALL the carbs off together to get to the middle one. So, you would need to do some prior planning before you start. I would suggest sealing all the carbs if they are off as preventive maintenance (one leaked so the others will too) so you will need three float chamber seals and three mounting gaskets at the very least.
If you don't own the HELM INC. official shop manual for your outboard, this would be an EXCELLENT excuse for getting one. It will make you MUCH more prepared and will probably increase your confidence in your ability for doing the job. That manual is a great INVESTMENT whether you do the work or hire someone. It will give you the information you need to make sure the job was done right. A Helm manual will pay dividends for "clearing things up" over the entire time you own the outboard.
I would certainly NOT be comfortable taking any boat out that had a fuel leak. Murphy's Law dictates that, not knowing EXACTLY when the leak will SUDDENLY get MUCH MORE SEVERE, it will probably happen with the engine at full throttle with your attention on steering and your back to the "problem" until the flames are REALLY high.
I was once trapped in a boat cabin by a fire from an alcohol stove between me and freedom. "No problem" I thought..."I'll just grab this here fire extinguisher, pull the pin and squeeze the trig......er...UH! WHOA!>>>>>
NUTHIN'!....YIKES!..... WE'RE ALL GONNA DIE!!!!!
Luckily, my buddy kept HIS cool, knowing that alcohol fires can be put out with water, he grabbed a big bottle of Aquafina and had the fire suppressed in a jiffy.
So, if you're thinking about taking an extinguisher with you and "chancing it" remember: gasoline CANNOT be safely put out with water and fire extinguishers don't always work.