Re: how does asprin act in the stomach with it being a weak acid?

There are at least two answers to your question depending on what you want 
to know.

First, because an aspirin tablet is made up with lots of other substances, 
when it hits the stomach, it needs to dissolve to free the aspirin.  
However, because the stomach is acid, the aspirin itself won't dissolve 
well.  The acid protonates the aspirin on the carboxyl group rendering it 
neutral in charge.  This is much less soluble than the ionized form.  
While the neutral form is actually the form that can be absorbed through 
the membrane, the surface area of the stomach is extremely small compared 
to the intestine and is not that well supplied with blood, consequently 
little aspirin is absorbed in the stomach.  However, because it cannot 
dissolve and because the undissolved aspirin also carries along some of 
the filler with it, it remains in tiny particles which irritate the 
stomach lining.  This isn't the primary cause of adverse effects of 
aspirin but does contribute to them.

Second, once aspirin passes through the stomach into the small intestine, 
the pH rises to 5.5-6.5.  At this pH most of the aspirin deprotonates, 
becomes ionized, and becomes very soluble.  However, there is still a 
couple of percent of neutral aspirin which can passively move through the 
membrane and then be absorbed via the portal vein into the blood from 
whence it goes directly to the liver.  (The charged/ionized form cannot 
readily pass through the membrane.)  Since this movement across the 
membrane removes neutral aspirin from the intestine, the chemical 
equilibrium between the neutral and ionized form of aspirin is changed and 
some of the ionized form will bind a proton to reestablish the 
equilibrium.  This goes on repeatedly until it's all absorbed.  In effect, 
the absorption of the neutral form drives the chemistry to make more 
neutral form in the intestine which gets absorbed, which makes more 
neutral form and on and on.

Third, now that aspirin is in the circulation/blood, some of it will reach 
the stomach and there will irreversibly inhibit the cyclooxygenase enzyme 
that makes the precursor to the prostaglandins.  Prostaglandins control 
and limit the amount of acid that can be secreted into the stomach when 
the body gets any appropriate stimulus (food for example).  If, because of 
the aspirin inhibiting the cyclooxygenase, you can't make prostaglandins 
in the stomach, then when the stomach is stimulated to make acid, there's 
no control, rather like having no brakes on your car.  This means there's 
a lot more acid in your stomach than there should be.  This can lead to 
ulcers which is indirectly the result of aspirin acting on the stomach 
cells and inhibiting prostaglandin synthesis.