I'd definitely advise against stopping weight training. I agree with runner83, in that this is probably a diet issue - it almost always is. In the short term nothing really makes a difference to weight like a correct diet.
Let's look at all the angles. First, unless you're bulking (eating more calories than you need to maintain your weight) your weight is not increasing due to weight training. In your first year, with a good diet you can expect around 2lbs a month of muscle growth (
http://www.bodyrecomposition.com/muscle-gain/whats-my-genetic-muscular-potential.html). If, as I hope, you're on a cut (eating less than maintenance calories), the reason you lift is to try to minimise muscle loss whilst you lose fat. If you're a beginner you may make a small muscle gain whilst losing fat...but I doubt it'll be more than 1lb a month.
You don't need to over do it in the gym though. 30 minutes with 1 set of compound lifts is really all you need to push yourself if you are a beginner. Until you've been training for 6+ months the benefit of multiple sets are negligible. Either way you don't want you gym time to be greater than 45 mins.
So onto cardio... Steady state cardio (aerobic running) was my bread and butter for a long, long time...but the reality is it doesn't burn an awful lot of calories. An hours worth wouldn't burn off a McDonalds meal for instance. If you're on a cut, then you risk this kind of cardio causing your body to enter catabolism mode - where your body breaks down muscle for energy instead of fat. Also steady state cardio doesn't actually help your heart and lungs as much as you'd think.
A better way is High Intensity Interval Training cardio. This is generally described as sprinting for a period of time until you die, then walking until you recover and repeating. But it doesn't have to be this hard. Run fast for 1 minute (so you can just complete it), then walk for 2 minutes. Repeat 10 times. You'll get a chance to drink some water in the walking period. As you get better, increase your running speed. You'll find this helps your heart and lungs no end, and your generally cardio fitness, as well as burning more calories than steady state (using the EPOC effect) whilst not wasting muscle.
You don't need to do any of this to lose weight though. Diet is king. I'd try tracking and weighing everything you eat and doing the math. When I came out of the Marines I put of 8lbs in a month - and none of it was muscle. I was working out 6 days a week but I wasn't doing anything like I used to. I was however still eating Marine style portions (~5000kcals a day). I had to cut back and start eating for my new energy requirements.