Factors which affect atomic radius are inner shielding and nuclear charge.
If you go across the period the atomic radius decreases due to an increase in nuclear charge so the outermost electrons are pulled much strongly to the nucleus. And the inner shielding doesn’t change significantly so that has no effect. When you go down the group the atomic radius, inner shielding both increase as well as the nuclear charge. However the combination of an increase in the atomic radius and inner shielding overrides the effect of nuclear charge.
Increasing the number of protons (nuclear charge) has two effects on the atomic radius but it all depends whether your going down a group or across a period.
Hope that helps!