The question is "does oblige share the etymology of obligate/obligation?"

Obligate has two different meanings...the most familiar, to bind legally or morally, or to commit; and the other, (pronunced with the short "a" --git) restricted to one particular mode of life, essential, necessary, an obligate paramecium.

Obligation, of course, comes out of the former, commitment.

From Merriam-Webster's:
Main Entry: oblige
Function: verb
Inflected Form(s): obliged; oblig·ing
Etymology: Middle English, from Old French obliger, from Latin obligare, literally, to bind to, from ob- toward + ligare to bind -- more at LIGATURE
Date: 14th century
transitive senses
1 : to constrain by physical, moral, or legal force or by the exigencies of circumstance <obliged to find a job>
2 a : to put in one's debt by a favor or service <we are much obliged for your help> b : to do a favor for <always ready to oblige a friend>
intransitive senses : to do something as or as if a favor

And, if so, how did oblige form off from obligate/obligation?

Or did I just answer my own question?

Some parasites may be able to survive without a host for some time, but many parasites can not, and so are obligate parasites.
As to range of meanings for the oblig- words, if you use "bind, bound" you can easily find many ways to use it. I am bound to bind my laces, lest in mid bound I become shoeless.

You prove my point dr. bill: I told you earlier today that despite age, you are still a bounder of the first order.

Then there's also noblesse oblige: [F, Lit. nobility obligates] the obligation of honorable, generous, and responsible behavior associated with a high rank or birth.

I hope WO'N doesn;t hate me for the diversion, but the word "bounder" interests me. I got the impression from way it was used in English novels that it suggested distaste for naive new students who exhibited too much enthusiasm, and then changed slightly to mean capable of unpleasant behaviour. What's your take on it?

"Bounder" has always meant a cad, an ill-bred oaf, someone maliciously acting outside the bounds of normal behaviour - or at least in my experience. That's the only way I've ever seen it used. Flashman in Tom Brown's Schooldays is a rather good example of one ...

I am bound to bind my shoelaces lest I become shoeless in mid-bound
Wonderful play on words, wwh, and most instructive too. I am bound and determined to match your bounding imagination but I am too hide-bound to escape my creative bindings.