We present a weak lensing analysis of a sample of SDSS Compact Groups (CGs). Using the measured radial density contrast profile, we derive the average masses under the assumption of spherical symmetry, obtaining a velocity dispersion for the Singular Isothermal Spherical model, $sigma_V = 270 pm 40 rm ~km~s^{-1}$, and for the NFW model, $R_{200}=0.53pm0.10,h_{70}^{-1},rm Mpc$. We test three different definitions of CGs centres to identify which best traces the true dark matter halo centre, concluding that a luminosity weighted centre is the most suitable choice. We also study the lensing signal dependence on CGs physical radius, group surface brightness, and morphological mixing. We find that groups with more concentrated galaxy members show steeper mass profiles and larger velocity dispersions. We argue that both, a possible lower fraction of interloper and a true steeper profile, could be playing a role in this effect. Straightforward velocity dispersion estimates from member spectroscopy yields $sigma_V approx 230 rm ~km~s^{-1}$ in agreement with our lensing results.
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