I am about to quilt my "sandwich" and will be using Black King Tut 40 wt thread on the top. I would like to use Libby Lehman's Black Bottom Line 60 wt in the bobbin. Is this too great a difference in thread weights? I want the quilting to show on the front, but not so much on the back.

Those two threads are a perfect combination

It sounds like they would be fine together.
We always quilted a little bit, then unzipped to look at the back. You may need to tweak your tension a little bit.

bottom line thread is used in bobbins all the time- and 60 wt just means you won't have to change the bobbin so often (it will hold more :)
people use all kinds of different combinations- invisible thread on top- bobbin wt on bottom- the same top & bottom-
silk in the top-
if it works for you and is a good thread- that doesn't break all the time- use it.
if you find you have all kinds of problems with it- then switch one or the other and try again.

Sounds like a great combination :D:D:D

mixing threads is done all the time It is fun to try different things and see the results. Have fun.