This paper presents results from the analysis of high signal-to-noise ratio spectropolarimetric data taken at four heliocentric angles in quiet-Sun internetwork regions with the Hinode satellite. First, we find that the total circular and total linear polarization signals vary with heliocentric angle, at least for fields with large polarization signals. We also report changes on the Stokes V amplitude asymmetry histograms with viewing angle for fields weaker than 200 G. Then, we subject the data to a Milne-Eddington inversion and analyze the variation of the field vector probability density functions with heliocentric angle. Weak, highly inclined fields permeate the internetwork at all heliocentric distances. For fields weaker than 200 G, the distributions of field inclinations peak at 90° and do not vary with viewing angle. The inclination distributions change for fields stronger than 200 G. We argue that the shape of the inclination distribution for weak fields partly results from the presence of coherent, loop-like magnetic features at all heliocentric distances and not from tangled fields within the field of view. We also find that the average magnetic field strength is about 180 G (for 75% of the pixels) and is constant with heliocentric angle. The average vertical and horizontal magnetic field components are 70 and 150 G. The latter (former) is slightly greater (smaller) near the limb. Finally, the ratio between the horizontal and vertical components of the fields ranges from ~1 for strong fields to ~3.5 for weak fields, suggesting that the magnetic field vector is not isotropically distributed within the field of view.