I've trained in shotokan karate and san soo kungfu for over 20 years. I took some time off while I was getting fat and lazy but have been training again for the last 3 years along with weight training. Go ahead and do both. Your martial arts training may cost you some size because of the intense cardiovascular workouts involved if you don't eat enough. But if you eat enough to support it, both types of training will be very beneficial. The improved balance and body awareness from the MA training will improve the quality of your weight training. The extra strength will improve your martial arts.
Many fighters will tell you that weight training isn't beneficial, or that you'll get muscle bound, or that if your technique is good you don't need to be big and strong...however, think about it - who would you rather NOT step into the ring with...two equally prepared fighters, exactly the same skill level, exactly the same quality of technique delivery, exactly the same speed. One is 130lbs, the other is 230lbs and shredded.
Just make sure you eat enough quality food and get enough sleep.
BTW, the extra size helps in other ways too. Last spring there were a couple of incidents where fighting was unavoidable because I weighed 170lbs, was outnumbered, cornered behind a gas station, and couldn't get away. The skills helped end it without getting hurt and I didn't have to hurt them too bad. They went to sleep and left me alone. Move forward in time to a couple of weeks ago, same punk, two different friends, similar situation. I was a bit over 200lbs then. One step towards them, the new friends said, "F*#! you man to the original punk and ran away, leaving him alone to run away too.
So the moral of the story is, "bigger is always better".