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?