You've got several issues operating, Victor. Let's take them in order.
1. Bolted Down Lathe. Your 750 is (I assume) on a component leg set (either Bill's or John's designs) which have some flex in the structure. That said, it is "popular learning" that bolting a wood lathe to the floor will cause early wear in the bearings because it channels most all of the work vibration to the bearings rather than allowing the energy to dissipate. This is somewhat opposed by more than a few machinists I've spoken to who site most industrial machines being floor mounted. They don't talk about doing so with a wood lathe, however. My S1000 is not bolted down (although my band saw is) and it's never been a problem. Being hyper-picky with leveling the bed in both directions is the key to a stable machine, and also functions as a safety feature for excessively out-of-balance workpieces. If your lathe starts to dance, it's time to slow down the music.
2. Remember as well that, while you own a beautifully made lathe with plenty of weight, it's not indestructible. The cast iron shell of your bed base is heavy and reinforced, but if you put so much stress on it that you force it to flex, you may crack that casting. Unbolting from the floor will prevent this scenario.
3. The tailstock and quill on your machine are easily heavy enough to handle much more weight than an 80 lb. piece. Part of your problem may (again) be due to the bolt-down (the stress has to go somewhere), but several other issues come to mind. First is that your center is not properly seated in the quill. This can be caused by not carefully cleaning the morse taper surfaces before insertion or by the presence of a bump or gall on either one. Careful inspection and cleaning of both will usually prevent this, but a gall must be removed. The male taper can be gently filed to remove a defect, but repair of the female taper will need a #2 morse taper reamer. ENCO sells them for about $30, and they should be basic equipment for any quality lathe. Second issue is over-extension of the quill. While that quill is plenty massive, it will flex if you're asking too much of it. For substantial wood in the beginning phase, keep it retracted as much as possible, and make sure that your bedlock is tight. Third, you should have your quill lock fully tightened as this eliminates any flex of the quill shaft inside the tailstock casting.
As an example, the attached pic is of a 25" rough of wet Sycamore just after being mounted on my lathe. The weight was well over 120 lbs., and had to be hoisted (power hoist above) onto the lathe. Note the short extension on the TS quill.
If this hasn't answered your problems, I suggest that you e-mail Bill or post the questions on the Stubby Group listserve.