Judo is an art of leverage, and the more strength you use, the less leverage, so it does affect your technique. The main advantage to you in weightlifting will be in groundwork and where you don't have leverage points to use.
Physical training methods have come a long way in the last 45 years, so weight training and flexibility are no longer mutually exclusive. Where once, if you lifted weights, you were stiff as a board, today... there is an equal amount of flexibility training added to keep you moving and strong.
The argument has been around forever, so I've never seen anybody that has either been too good to use their strength, or been so strong that they didn't need their technique. It's a matter of personal choice, and if you understand that if you start down that road and suddenly stop, it will cause your body to crash, go for it. There is a limited amount of weight training that is necessary for any strength-flexibility sports, and Judo is no different. If you choose to add weights to your regimen of training, go for it... just try to remember that Judo works off technique, not strength... and the old rule of learning some technique before getting strong isn't a bad one. It only makes you better in the long run.
By the way, if people have been training longer than you, they SHOULD be better than you if they're doing it right... so don't think that you will overcome them by simply getting stronger. Some of the most wicked throws in Judo are some of the sacrifice throws, which take no strength... such as the side-separation.
If you'll spend most of your time gaining ukemi skills, you'll get a feel for most of Judo from the falls... that is what teaches you how to do throws in most cases. Lots of "fits" and "uchi-komi" will help too...
My .02 worth...
