An investigation of symmetry breaking and naturally occurring instabilities over thin slender delta wings with sharp leading-edges was carried out in a water tunnel using Particle Image Velocimetry (PIV) measurements. Time-averaged location, strength and core radius of conical vortices vary almost linearly with chordwise distance for three delta wings with 75o, 80o, and 85o sweep angles over a wide range of angles of attack. Properties of the time-averaged vortex pairs depend only on the similarity parameter, which is a function of the angle of attack and the sweep angle. It is shown that time-averaged vortex pairs develop asymmetry gradually with increasing values of the similarity parameter. Vortex asymmetry can develop in the absence of vortex breakdown on the wing. Instantaneous PIV snapshots were analyzed using Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD), revealing the shear layer and vortex instabilities. The shear layer mode is the most periodic and more dominant for lower values of the similarity parameter. The Strouhal number based on the freestream velocity component in the cross-flow plane is a function of only the similarity parameter. The dominant frequency of the shear layer mode decreases with the increasing similarity parameter. The vortex modes reveal the fluctuations of the vorticity magnitude and helical displacement of the cores, but with little periodicity. There is little correlation between the fluctuations in the cores of the vortices.