Aims.This paper is devoted to an interpretation of Quiet-Sun, spatially-resolved spectropolarimetric observations of the Hanle effect in terms of turbulent weak magnetic field determination. Methods: . Observations: the slit was positioned perpendicular to the limb, and the spatial resolution along the slit was 1 arcsec, leading to a depth probing along 132 different limb distances. The new polarimeter of the Pic-du-Midi Turret Dome was used on May 14, 2004 to observe a quiet region at the East limb equator in the resonance line of neutral Strontium at 4607 Å. Results: . For each limb distance, we properly adjusted the theoretical intensity profile obtained by applying a zero-field model to the observed one. Micro- and macroturbulent velocities were thus derived (average values v{micro}=1.77 km s-1 and v{macro}=1.95 km s-1). The magnetic field was determined in a second step by interpreting the Hanle effect on the line center linear polarization degree. The depolarizing collisions with neutral hydrogen were taken fully into account through a semi-classical calculation of their rates. An average value of B=38 Gauss was thus derived. Finally, error bars on the magnetic field values were evaluated from a) the polarimetric inaccuracy, b) the limb distance determination inaccuracy, and c) the uncertainty on our theoretical collisional depolarizing rates that we evaluated. This combination leads to 10-20% as total relative error on the magnetic field determination by the Hanle effect method. Since the inaccuracy due to the model itself was hard to properly evaluate, it was ignored. An uncertainty of ±60 km on the line formation depth was, however, derived from the contribution functions. The magnetic field is found to increase slowly with height in the height range 220-300 km above τ5000=1 and then decrease in the height range 300-370 km.