What is the fastest way to level a weapon/Warframe?

I want to raise my MR but I like using the stuff that I like. Leveling up this damn karak has been hell. I don't like running high level missions on public and just being dead weight, but I also don't want to use stuff I hate. Im so limited by my MR. I have a riven for my catchmoon but it feels like I may never be able to use it. For some reference, I can take down an eidolon teralyst pretty handily solo, and can get through around level 80 missions (also solo), but I just hit MR9 after probably 80-100 gameplay hours at MR8. I accidentally entered an ascension mission with a rank 6 weapon once and it was at 30 after, but that was the nataruk so it was already actually useful at low rank. Don't wanna just leech off of people who are trying to speedily farm missions.