One critical factor in determining the strength of acids can be the strength of the HA bond.  Clearly if the proton is very tightly held by the rest of the molecule, it will require a lot of energy to remove it, and hence the acid will be weak.  Equally, a weakly-held proton is a characteristic of a strong acid.

The above equilibria illustrate the point.  CH₅⁺ (which can be made, and is used in the gas phase to protonate virtually anything, as a very strong acid) does not have a particularly strong bond to the proton.  However, all of the CH bond in methane are much stronger, and hence more difficult to break. Thus methane itself is a very weak acid.

Obviously, to present these as the only considerations is misleading, as there are other factors such as the relative stabilities of acid and conjugate base.

Consideration of the HA bond strength alone is rarely useful.  It does make sense, however in certain instances, such as the halogen acids: HF, HCl, HBr, HI (although even here it is not the only factor), as the acid strengths increase with decreasing bond strength.

The other main factor involved here is the better charge distribution on the larger anions.