Obligate
In AWE's view, the English verb 'to oblige' is usually preferable to 'to obligate'. The simpler word is better, where there is no marked difference in meaning.
The New Fowler's Modern English Usage, Oxford University Press 1968, says that
"it ['to obligate'] is not now found in standard use in British English, having been replaced in all main uses by obliged. It is a routine example of a word that was once (17-19c.) standard in British English but has retreated into dialectal use, while remaining common (beside obliged) in American English and to some extent elsewhere".
OED gives the earliest occurrence of obligate as 1541, and in the sense 'to oblige' 1668; whereas the earliest record of oblige is 1297. OED comments in its list of meanings of obligate "5. a. = OBLIGE v. 6, 7. (Not now in good use.) In later use chiefly dial. and U.S. colloq."
AWE advises British students to use 'to oblige' in preference to 'to obligate'.
(It may be of interest to know that the accepted 'proper' pronunciation was 'uh BLEE ge' (IPA: /ə ˈbliːʒ/, in the French style, until after the beginning of the 19th century.)