That problem of mine was two-fold. First off, I wasn't very good at throwing a weapon shot. A year later, and I'm still not great at it, but I'm getting there. So, my damage output was lacking, because of my swings, and how unskilled they were. Compounding that issue was my hatchet and buckler. Early on, a loaner weapon that was available to me was a one-handed axe with a tomahawk type head, and it was fairly small and light. In my other hand, I held the free buckler I was lucky enough to get packaged in with my armor when I bought my kit. I was clinching a lot in the old days, relying on my rusty Muay Thai skills to survive. I rarely had a chance to use my weapon and shield, beyond the occasional buckler punch to the face. When I found myself surviving the scrums more and more, I also found myself with an exposed opponent's back. I needed to try something new.
First step was turning my buckler into a more offensive weapon. Cat Brooks developed what we affectionately call the “Punch Buckler,” (a strapped version of the classic buckler). There's advantages and disadvantages here, but personally I love it. A small, metal shield turned on it's edge is almost like punching with the striking edge of an axe. It can slip through defenses like a jab, and can find open spots like a weapon strike. It's small enough that it doesn't get tangled up in a grapple. And, it's still a shield; I've got creases on it to show where I've caught a two-handed strike.
Next was trying to figure out my main-hand weapon. Early on, I was barely using my weapon at all. So it seemed a no-brainer to stick a heavier axe in my hand, so that when I did swing it, I did it with some meaning behind it. It worked just OK. The “dread axe” head that is so popular as a two-handed axe head these days was my one-handed axe, and that was a mistake. It was too heavy, I couldn't get any snap to it. The plus side of the weapon was that when I got ignorant and desperate, I could slide my hand up and punch with it. That happened more than I'd like to admit.
I've since changed to a falchion. It's the same weight as my axe, but more evenly distributed throughout the weapon. I've been fighting with it for quite a while, and I still feel like I'm learning. But it's quicker, has a bit more reach, and is easier to toss out a quick slash. Then, when I want to switch to a more offensive output role (like a teammate is tangled with an opponent, and I have their exposed side), the falchion has enough weight so I'm a threat.
That's a step forward, but I'm by no means done experimenting with weaponry. I talked mostly about one-handed weapons here, and that's because my two-hander skills are far behind my other skills. I've played with them in melee and found myself holding it in one hand, and punching with the other. Brandon Ross, my brother and captain of the Knightmares, took to a two-handed weapon like a natural. He quickly found out his college baseball skills were translating into power generation, making his two-handed hits brutally effective.
Don't ever stop experimenting with weapons. Some fighters fall into the trap of “I'm worried if I switch I'll be at ground zero again,” and that is partly true. But the benefits of finding a weapon that fits your style outweigh the risks. Switch weapons with your training partner. Goof around on the pell with something you borrow for the day. Explore all options, because you might find the perfect thing out there for you. And worse case scenario, you get a little experience with a variety of weapons, which is never a bad thing.