We examine the morphological and statistical properties of close galaxy pairs from two sets of 28 WFPC2 fields, acquired for the Medium Deep Survey (MDS) and the Groth-Westphal Survey (GWS) in F606W (V) and F814W (I) passbands. In the GWS sample all fields have uniform 95% completeness down to I <~ 24.3 mag, whereas in the MDS sample, fields have varying 95% completeness limits in the range I <~ 23.6-24.8 mag. In each field ~400 galaxies per ~=5 square arcmin field are detected. We exploit high-resolution WFPC2 images to systematically determine morphological classifications of galaxies as disk or bulge dominated down to I <= 23 mag (V <~ 24 mag) and to differentiate galaxies from stars 1 magnitude fainter. Down to I <= 25 mag the number of galaxy pairs with separations θ <= 3.0" is consistent with a shortward extrapolation of the angular two-point correlation function ω(θ) ~ θ-0.8 observed from the same data; the fraction of such pairs showing morphological evidence for physical association accounts for a third of the total numbers suggested by a shortward extrapolation of ω(θ). The latter result may not be too surprising given the low surface brightness of the tidal tails resulting from galaxy interactions; i.e., much of the evidence for interactions may fall below our detection limit. Moreover, we find no trend between apparent physical association (on the basis of morphology) and (V - I) color or I-magnitude difference between pair members of the θ <~ 3.0" pair sample.We use recent galaxy redshift surveys to estimate the rate of galaxy merging occurring in the MDS and GWS galaxy pair samples. From this work we find that merging has a moderate dependence on redshift: we derive an estimate for the galaxy pair fraction Pf ~ (1 + z)m, with m = 1.2 +/- 0.4 for galaxies with I <= 25 mag (zmed <~ 1-2). Two scenarios are consistent both with this low value of m and for the low correlation amplitude: (a) a low-density universe with strong clustering evolution parameterized by a clustering exponent e ~= 1.0 such that galaxy cluster-scale structures shrink relative to the proper coordinate frame; and/or (b) a weakly clustered galaxy population, the majority of which fade or dissipate below zmed <~ 0.5 (I <~ 20 mag), thus mimicking the apparently strong evolution in the correlation amplitude, Aω. Although not directly observed using our data, the possible flattening of the slope of ω(θ) with increasing survey depth can explain the strong decline in Aω and allow for greater pair fraction evolution limited to m <= 1.6. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.