Riccia doesn't root so if you tied it to anything, it will just keep growing into a bush until you trim it. It may spread horizontally, but it won't ever attach to the wood.
It is a pain and a mess! I had to give up on it.
Baby tears (Hemianthus micranthemoides) grows healthier in medium to high light with co2 and fertilizer dosing IME. I have had it in medium light with no co2 injection and no fert dosing and it grew ok....just slow and some didn't look good.
I suggest putting it in a more lighted area, spread it out a little it you haven't already and hopefully it will start to look better.