Hey Laggard,
Just as some of the others before me have mentioned, sweating is your body's way of keeping cool and releasing toxins. Since you mentioned that you had a physical recently with good results, your blood pressure and cholesterol are low and you are in overall good shape, I honestly don't think that the sweating is something to be overly concerned about. I am not a physician or licensed personal trainer, but I am a certified fitness instructor, and I know large amount of sweat during a difficult exercise is normal. ( I personally sweat buckets on the elliptical if I push myself hard)
If this really is a new problem that is bothering you, I would suggest (like rofl1 said) to think about what you ate and drank earlier in the day. Drinking lots of water may cause you to sweat more, because your body is well hydrated and able to sweat to keep you cool. Also, eating fatty foods may increase your sweat output since your body is working hard to digest the food. Another factor that may have caused this rather sudden increase could be new medication. I have noticed that in some people, certain medicines (often medicine like adderall) can really increase a person's sweat output. While I have no idea why this happens, I have seen it.
Be sure to be aware of your body, immediate changes and the things you put in it. Profuse sweating is a symptom of heat exhaustion (while I don't think this is happening to you) be aware that if other symptoms such as pale, cool, moist skin, muscle cramps or pain, headache, dizziness or nausea happen in addition to your sweating, you should bring your heart rate down, seek medical attention and rest immediately.
As embarrassing as extreme sweating can be, it normally isn't something to worry about. Plus, you haven't had a good workout if you still look great after doing it! haha. Be sure to shower after you finish working out to keep your skin clear and pore unclogged, drink plenty of water, keep a towel with you and turn on the fan if you need!
Sounds like you are a healthy man, so keep up the good work!!
--I am not a medical doctor and the post above is my personal opinion. Please consult your physician if you are truly worried about any medical issue you are facing--