I have an Osage stave I've been practicing technique on. It split asymmetrically and one limb was very thin.  By the time I cleaned it up and balanced the two limbs, it's about 60" long. Barely 1.25" at the handle and tapers to .75 " at midlimb and 0.5" at tip. Being so narrow, would a rounded limb cross section be better than a flat limb design?

I would say yes, rounded.

Thank you.

How thin or how narrow?

The limbs are narrow. Talking width not thickness. Sorry.

I like 1 3/8" wide for any osage bow. 1 1/4" will work too. I've made quite a few 1 3/8" x 60" osage selfbows in the 45# to 60# range. Also, IMO osage likes a slightly rounded belly. It can handle the concentrated compression stresses and performs well with a rounded belly.

This stave is 1.25 at the handle but begins tapering immediately. It's about 3/4" at midlimb and 1/2" at tips. Just the way the log split didn't leave much at the one end. We'll see what happens. I'll do a rounded belly.  Thanks for tips.

I have made 2 bows barely 1" wide and and 60" long that made 60# at 28".

I'd make the bow 3/4" wide for as long as you can and try for an English Longbow style.  In other words, almost as thick as it is wide.

I made an osage sucker bow that was an inch wide that came out 49#. Jawge