Re: do weak acids produce more OH- than strong ones?

In general, when chemists speak of acids they talk of the acid's ability 
to generate H+ (a proton) and not so much about how much OH- is present in 
solution (usually an aqueous solution).  If a solution is acidic, then you 
will be measuring the H+ concentration as acids generate protons and not 
hydroxide ion (OH-).  When dealing with basic solutions (such as an 
aqueous solution of sodium hydroxide), the amount of OH- becomes 
important.  Strong acids are characterized by their ability to generate a 
lot of H+ and include hydrochloric acid, sulfuric acid, and nitric acid.  
Weak acids are able to generate H+, but not nearly as much as much as 
strong acids.  Weak acids include acetic acid (vinegar), formic acid, and 
carbonic acid (which is present in soda). 

Why is a weak acid weak?  It has to do with what happens when the proton 
leaves the rest of the molecule.  The part of the molecule that remains 
after the proton leaves is called the conjugate base and usually has a 
negative charge, though it can be neutral in some cases.  If the conjugate 
base is exceptionally stable in solution, then it is easier to 
dissociate.  The hydrogen sulfate ion (HSO4-) is the conjugate base of 
sulfuric acid, and is extremely stable, making sulfuric acid very strong.  
The carboxylate ion (H3CCOO-) is the conjugate base of acetic acid and is 
not as stable in solution – it would rather be bound to its proton.  The 
reasons for the stability or lack of stability involve something 
called "resonance" and is too advanced for our discussion here.

There is some math and experimental work involved in determining whether 
an acid will be strong or weak, but it, too, may be more than necessary 
for this explanation.  If you are interested, I would suggest reading an 
introductory general chemistry book or the following website, which has an 
excellent explanation of the basic math behind acid/base chemistry 
(http://en.wikipedia.org/wiki/Acid).