If you look at a Lewis Dot structure of the haloacids (HF, HCl, HBr, HI), you'll see that that the acidic hydrogen is directly bonded to the halogen anion. The reason for why the haloacids get stronger down the group is because as the ionic radius of the anion increases, there is less orbital overlap between the halogen anion and the acidic hydrogen. Thus, with less orbital overlap the H-A bond is weakened, and the haloacids of larger anions lose their acidic hydrogens more easily.
If you observe the Lewis dot structures of the oxoacids (HClO3, HIO3, etc.), you'll see that the acidic hydrogen is bonded to an oxygen atom, not the central halogen anion. Thus, there is no significant change in the orbital overlap between the acidic hydrogen and the anion, as the bond is always between the hydrogen and an oxygen atom (O-H bond). Therefore, the most significant factor is the change in electron density around the acidic O-H bond. As one moves down the group, elements generally become less electronegative, and thus are not as good at drawing electrons towards themselves. The oxoanions of more electronegative elements thus are better at drawing electrons from the O-H bond and towards the main body of the large anion. As electron density around a bond is a good measure of the bond strength, we can conclude that the O-H bond is weaker in oxoacids made of "more electronegative anions" (even though I think you technically can't call an anion electronegative). The same reasoning applies to oxoacids with more oxygen atoms than others, because the increased number of electronegative oxygen atoms draw electrons away from the acidic O-H bond.
As a recap:
- ionic radius is the primary consideration for acidity in haloacids
- electronegativity is the primary consideration for acidity in oxoanions