Ya'll can laugh at me if you want. I have maybe a strange question.

When positioning yourself on your saddle, how do you actually sit? Do you let your "package" hang to the right, left or do you prop it right up on top the seat in the middle. If I go left or right then one side of my butt gets fatigued with it. I don't think I am larger in that area than average. Am I missing something? Nobody has ever been willing to discuss this with me. Meanwhile, my junk suffers. I am a bit of a novice to riding distance, am overweight but don't want to let that stop me from enjoying my rides.

I sit my bones on the wide part of the saddle, just behind the nose that supports the . . . soft tissue. This is on my mountain bike. The saddle I use has a groove down the middle to alleviate pressure there, as I was having numbness problems with the standard saddle.

On my road bikes I tilt a lot more forward, so the front of my pelvis would push the soft tissue into the nose of the saddle. Not good. In order to alleviate that, I use ISM Adamo Road saddles, which have two "prongs" instead of a regular nose. The prongs support my pelvis directly. That kind of a saddle (Cobb is the same way) is designed for triathletes and time triallers who are down in an aero position a lot. They aren't comfortable (for me) to use with an upright position.

You will need to be centered and symmetric on the saddle, or you will get who knows what kind of joint and/or back problem from riding crooked. Read: pain.

Make sure your saddle is mounted level (or as directed by the manufacturer), is at the right height (leg not quite straight at the bottom of the stroke), and is positioned right horizontally (plumb like from kneecap should go through pedal center at 3 o'clock). These are just starting points.

I'm guessing you aren't wearing cycling shorts. Shorts and bibs are snug enough to help hold your stuff in place.

No one, man or woman, is perfectly symmetrical. You can angle your saddle slightly to on side or the other to relieve some pressure.

The OP is talking about sitting crooked on purpose to avoid circulation problems, etc. That's not a good plan.

But you're right about the asymmetry. With a new saddle I generally start with it straight and then ride to town or something (maybe 10 miles) and watch where my knees end up once I have the feel for that particular saddle shape. Generally I end up rotating the saddle just a teeny bit.

One thing you do not want to do is adjust your saddle to accommodate an asymmetrical form. Better to fix the form first and then worry about fine tuning the saddle.

It's the same way with nose up or down. Some saddles work best level across the top, but different body shapes and/or riding styles dictate a little tilt one way or the other. The Adamo Road saddles I use are supposed to be installed at first with the rails level which leaves the top tilting down quite a bit. It's just the way that saddle is shaped.

As noted, a good pair of bike shorts provides considerable support and comfort. I find angling the nose of my saddle just slightly down from level is about right for me.
Make sure, as noted, that you're actually sitting on the saddle properly...With your "sit bones" firmly on the most-padded area of the saddle.
As well, make sure the fore-and-aft adjustment of the saddle is correct. Too far forward or too far back can cause problems for your sitting position and your knees as well.