The rhubarb is floating to the top of the jar. Do I need to use weights to submerge them?

It should be ok but you can always put it in the fridge if you're worried.

You might want to transfer to a larger jar and put a ziplock bag partly filled with vodka on top to submerge the rhubarb pieces. If the bag leaks or ruptures, you'll just dilute the infusion a little bit but no harm will come.

I do this when I'm making kimchi in a large jar; I fill the bag with 2.1% brine (same salinity as the kimchi itself) to ensure the ingredients are fully submerged since it's an anaerobic lactic acid fermentation.

Best of luck.