I have a weakened villager because of bites and I haven't gotten the second exploration tech yet so I can't make a stew for her. So my question is what do I do to keep her from dying?

If you keep dragging her to the food bin she will eventually gain all her health back. This does take time and a bit of food but eventually she will gain full health.

And let the villager rest...

and set him as Farmer, it's less difficult!

And as a farmer they will not get hurt as much or take the villager and keep putting him/her onto the food bin.