For chucking weighted nymphs and Wooly Buggers around an 8 1/2 or 9 ft 5 wt rod would be better.
If someone is going to own just one fly rod, I'd recommend and 8 1/2 ft, 5 wt. It's pretty versatile.
With the rod you have, you might try a few things:
Making the leader a little shorter if you are throwing weight, as compared to dry fly fishing.
Use flies that sink efficiently. For example, a beadhead pheasant tail nymph is sleek and isn't made of bouyant materials so it sinks better than a fuzzy Hare's Ear. Copper Johns also sink very quickly without adding a lot of additional weight.
With streamers a Clouser Minnow sinks much better than a Wooly Bugger, for the same reasons.
As Chaz said, the casting stroke when casting weight is very different from casting dry flies. You want to slow down your casting rhythm. Be sure the line and leader fully extend on the backcast and the rod is fully loaded (bent under the load of the line and weighted flies) before making the forward cast.
Then you start the cast slower than usual, to allow the rod to recover, because it's bent more than usual from the weight. Then as you feel the momentum of the weight moving foward, then you SEND IT, that is you put a lot of power and speed into the last part of the forward cast.
Think of a pitcher throwing a baseball. It's pretty light so he can really fire it. But then compare that with someone throwing a shot put. It's very heavy, so the shot-putter has to start the movement slowly, to get that weight moving, then after it is moving he accelerates his speed to get the weight moving faster and at the end of the movement he is throwing as fast and hard as he can.
It's the same when throwing weighted flies. You start the forward cast slowly, to get that weight moving, then you put the power to it.
You are SLINGING the lead weight basically. You use the momentum of the split shot or weighted eyes to carry the cast out there.