Your phrase
slightly too weak
is perfectly understandable and correct with the meaning of
weaker than weak, but not quite as weak as too weak
The car is slightly too weak to pull the boat, if the boat was 10 pounds lighter it would work.
At 4 foot 11 inches, David is slightly too short for the 5 foot ride.
In order of weakness
weak
slightly too weak
too weak
just as in
expensive ($100)
slightly too expensive ($500)
too expensive ($1,000)
much too expensive ($10,000)
very much too expensive ($100,000)
Holy Cow! ($1,000,000)
The use of "slightly" (less) partially cancels out the use of "too" (more).