Neither of your natural-sounding examples has an indefinite article followed by a time unit followed by "before" within an "if" clause. It seems to me that one or more of these factors must be contributing to the difference we sense.
"I think we have met before" has no article and time unit, so I think it's a different case of "before" meaning "on another (previous) occasion". There's no attempt to say how long before this utterance the meeting actually occurred.
"I think we have met a week before" is impossible (a definite time together with the present perfect tense), and "I think we had met a week before" again sounds strange in the way that "if you had left there an hour before" does, especially when contrasted with the better-sounding "I think we had met a week earlier" or "if you had left an hour earlier".
"It had been fine the week before" also differs from the strange examples. This time the difference is in the use of the definite article "the" rather than the indefinite "a(n)". "
the week before" indicates a certain period of time
during which it had been fine. Changing to "a week before" gives "It had been fine
a week before", which indicates a point of time
at which it had been fine.
Now "it had been fine a week before" may or may not sound as strange to your ear as the other examples. If not, then it may be due to the change from dynamic verbs (left, met) to a stative verb (been). Another puzzle to solve!
Generally, it seems to me that "the [day / week / ...] before" and "a [day / week / ...] earlier" are the pairings that work best, i.e., "during the previous period with a length of one [day / week / ...]" and "at a point in time one [day / week / ...] before the reference time".
This analysis has now, I think, reached the point of diminishing returns.