Your veterinarian is absolutely right. He will have to be neutered sooner or later, and sooner is safer. In intact male dogs, the prostate usually swells with age. Neutering stops that. They can get infections and other problems with the enlarged prostate. That right there is a reason that older males tend to get neutered, if it wasn't done when they were younger.
One testicle larger than the other could even be cancer, or precancer. Ask your veterinarian if the tissue should be sent to a pathologist after the neutering, so you'll know to watch for further signs if it is cancer.
I would not wait on doing this. Do have bloodwork done prior to surgery, because at that age they need to check to various things to make sure the dog is a good candidate for surgery. That bloodwork will make a valuable record for later in the dog's life, too.
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Kathy Diamond Davis, author, "Therapy Dogs: Training Your Dog to Reach Others," 2nd edition, and the free Canine Behavior Series articles at http://www.veterinarypartner.com/Content.plx?P=SRC&S=1&SourceID=47