DRIVE SHAFTS....

I am in the process of wrapping up my 77 LeBaron 7.25 conversion to 8.25. The last item I needed was a drive shaft for this specific application. I did indeed find one.
It was a bit of a mess requiring several hours worth of cleaning, painting and prep for new u-joints. While doing so, I noticed something on the shaft itself. There were
no balance tabs welded on the shaft and looks like never were. So my question is, have any of you seen any Mopar factory drive shafts that hadn't had any factory
balance weights welded on them?? I can only assume at this point that the shaft was true enough and didn't need further balancing.

I can't speak to the factory "how many would have had a balance weight" question, however you can get this one installed and do a quick check whether you've got a problem or not - and this won't require a test drive either.

Put the rear axle on stands, tires off of the ground, put some wheel/tire blocks on the front tires (man, safety first), toss the thing in gear and gently bring up the speed. That will give you a sense if anything is off.

Next, get it back to idle, pop the hood, get that carb onto FAST idle setting, just watch the speed carefully, and now you're going to climb under the car (as the shaft is spinning, and so are the wheels), gently bring up a wax pen, or some kind of a marker up to the driveshaft body as it spins, let it gently make contact with your marker.

If there is a visible 'high spot' it may indicate either an offset shaft or off-balance shaft, and that is WHERE the driveshaft will contact your marker.

That'd be your indicator that something is in fact off.

The next step of troubleshooting this is written up pretty well in the FSM, basically bring everything to a stop, put some steel bands on that, move the bands around as you repeat the whole process and you figure out WHERE that weight should actually be located.

To be honest, it all sounds easier said than done. I am very uncomfortable under the car when things are moving and my ride is just in my garage, so while doable I myself would rather recommend that you bring your shaft to a local speed/driveshaft shop and simply have them put it on the balancer and check.

Heck, I just had the front and rear U-joints re-done on my custom made shaft (so 2 new U-joints and 1 new trans slip yoke), balanced and that was $175 out the door!!!

Thanks for the reply and suggestions. Factory SM does tell how to balance as you've suggested.
BUT,......is it probable that there was never ANY balance weights on the shaft simply because the shaft
was true enough?? Again,. there is NO visible area where ANY weights were ever applied.

The weights usually gave a single spot weld holding them on. It probably is possible that it never needed it or that it got rusty and popped off at some point. It would be hard to notice unless you knew where it was.