Acids come in different strengths so the amount of H+ that can be released relative to the total concentration of the acid compound is highly variable. Basically, the idea is that "acid" means that there is a favorable condition for releasing an H+ from the rest of the compound. Water is an acid, even. Its pH is 7. It isn't a very strong acid (hardly lets go of the H+ unless really forced to). Some acids, like HCl, though, have almost no hold on the H+ and will lose it easily, and acidify water a lot.

All by itself, the pH of water will be (about) 7, what we call neutral. Very weak acids tend to be made from strong bases (strong bases GRAB loose H+ if it is around), and strong acids when combined with strong bases, tend to make salts and water (like HCl (strong acid) reacts with NaOH (strong base) to make H2O (water) and NaCl (table salt); a solution with a near neutral pH).

In the bulk mix of compounds that is the natural world, and the human body too, the mixture of strong acids, weak acids, strong bases, and weak bases, and other things with effectively no acid behavior at all, when all the competition is done between the various species for grabbing or releasing an H+, the system tends to end up somewhere around neutral. The system "wants" to go to neutral if it can, basically. Strong bases grab H+ just as much as strong acids release it. The end balance in most systems sees this happen, and near-neutral is the result (just as likely to see a strong base as a strong acid, and the two coming together makes a neutral salt and water).

That is the basic reason that the human body is slightly above neutral in pH. It is mimicking (trying to reproduce) the natural world, the ocean that life came from or developed in, originally, which is slightly basic too.

What is an amino acid? They are basically ammonia (NH3) where the H atoms have been replaced, at least in part, by some other large chemical group, many of which are weak acids. We call such compounds "amines" (hence they make "amino" acids), because the nitrogen is in the reduced state (filled to max with electrons, hasn't met other elements that want its electrons even more than it does itself). When reduced nitrogen does meet a strong electron grabber like oxygen, it makes nitrates (and nitrites, sort of the same thing), but that is a little off where I am going with this explanation.

The amine groups tend to be attached to weakly acidic other compounds, or rather weak acids like HCO3-, so one side of the compound is a weak acid, but the other side, or sometimes inside (if all H+ has been replaced by weak acids), it is a strong base. So, because the primary characteristic is a weak acid, the compounds are "amino acids". However, they are not strong acids at all, they are weak acids and do not lower pH by much. If they had been stronger acids, they would have reacted with ammonia to make NH4+ (would have just told ammonia, here is the H+, take it and leave us alone out here in weak base land away from you).

Amino acids are, in effect, the result of that pH-balancing process that happens in nature. The amine group is, if in its normal state of ammonia (NH3), a very strong base. It wants to make NH4+ by grabbing any H+ it can find. the end result is that it sort of does do that, by grabbing on to other compounds that have a weak grasp on an H+, changing the product into a very weak acid rather than its once powerful base. When together, these combined molecules are pretty "happy" in near-neutral conditions. The strong base (ammonia) was neutralized by reacting with acids (like carbonic acid) and now we have a happy "acid" that is not very acidic in behavior, it is very weak. And there are still some bases out there floating around, not strong enough to grab H+ from the weak amino acids, but plenty strong enough to grab H+ from some stronger acids, if they come along, and in so doing, neutralizing them.

So, the system is happy and near neutral. It is where things, taken all together, tend to go to be in balance, somewhere near neutral pH. The world likes to get into some sort of middle balance if it can.