I make my own sauerkraut. I've been doing it for about a year now. Here's how I do it:
- I cut the cabbage into chunks.
- I put those chucks through the food processor to shred them (because I'm lazy and don't want to chop it all up myself).
- I dump all that in a bowl and add whey (from yogurt) and sea salt and red chili pepper.
- I use clean hands to mix it all and massage it.
- I stuff it all into widemouth jars (6" tall by 4" wide or so).
- I add a little water to the top.
- I seal the lid and place them in a warm place for 3 or 4 days (with a piece of tape on them reminding me when to move them).
- I move them to cold storage (fridge).
Never in that process do I use a weight or a plate. I've never found that I need to keep my cabbage below the brine. It kinda does that on it's own while it ferments (because the salt is drawing the moisture out). And it leaks, so I keep the jars in little plastic bowls.
All that said, trying a french press might work too! ;)
P.S. Sometimes I use raw apple cider vinegar instead of whey. Works like a charm!