Why does mercury form polycations?
I don't have an excellent understanding of the topic, but I will try to write something up.

Polycations are found with the Hg(I) oxidation state. The mercury cation, $\ce{Hg+}$, has a $\mathrm{5d^{10}6s^1}$ configuration. The mercurous cation $\ce{Hg2^2+}$ can then be considered to simply be formed by overlap of the two $\mathrm{6s}$ orbitals on two separate $\ce{Hg+}$ ions. In this sense, the bonding is qualitatively very similar to that in $\ce{H2}$. Note that the $\mathrm{5d^{10}6s^0}$ Hg(II) cation has no chance of forming such covalent bonds.

Generally, going down a group, orbitals become larger, more diffuse, and the overlap between them decreases. As a consequence, $\sigma$-bonding tends to become weaker going down the group. A simple example is provided by the alkali metal dimers:

$$\begin{array}{c|ccc}
\text{Element} &amp; \ce{H} &amp; \ce{Li} &amp; \ce{Na} \\  \hline
D_\mathrm{0}(\ce{E-E})\text{ / }\pu{kJ mol-1} &amp; 432 &amp; 99 &amp; 71 \\ \hline
\text{Reference} &amp; 1 &amp; 2 &amp; 3
\end{array}$$

These dissociation energies are extremely small. For the analogous $\ce{Hg2^2+}$ cation, the situation is not quite as bleak. The Group 12 metals in general have more low-lying and contracted ns orbitals than the corresponding alkali metals, due to the presence of ten poorly-shielding (n-1)d electrons. However, given that zinc does not form similar cations, it is odd that mercury with its larger 6s orbitals should do so.

The most obvious explanation is simply that Zn does not commonly exhibit the +1 oxidation state. The existence of the +1 oxidation state for Hg is directly related to the relativistic stabilisation of the 6s orbital, which increases the first two ionisation energies4 of mercury.

$$\begin{array}{c|ccc}
\text{Element} &amp; \ce{Zn} &amp; \ce{Cd} &amp; \ce{Hg} \\ \hline
I_1\text{ / eV} &amp; 9.393 &amp; 8.992 &amp; 10.44 \\ \hline
I_2\text{ / eV} &amp; 17.96 &amp; 16.90 &amp; 18.76 \\
\end{array}$$

However, the question still remains as to why Hg(I) chooses to form polycations instead of existing simply as $\ce{Hg+}$. In fact, relativistic effects have also been implicated in this for a long time: Pyykkö and Desclaux wrote in 1979 that5


  The relativistic contraction of the half-filled valence s AO makes $\ce{Au2}$ much more strongly bound than $\ce{Ag2}$. Inasmuch as $\ce{Hg2^2+}$ and $\ce{Cd2^2+}$ are isoelectronic with these two molecules, the remarkable stability of the mercurous ion [compared to the Cd analogue] can also be understood.


Therefore, this may most simply be explained as the relativistic contraction of the 6s AOs leading to stronger-than-expected overlap to form a covalent bond. As suggested by the above paragraph, similar effects are seen in the neutral dimers of Group 11 metals:6

$$\begin{array}{c|ccc}
\text{Element} &amp; \ce{Cu} &amp; \ce{Ag} &amp; \ce{Au} \\  \hline
D_\mathrm{0}(\ce{E-E})\text{ / eV} &amp; 1.95 &amp; 1.65 &amp; 2.29 \\
\end{array}$$

The decrease going from Cu to Ag is expected on the basis of weakened overlap, and the dissociation energy of $\ce{Au2}$ would be even lower in the absence of relativistic effects: calculations indicate that relativity contributes roughly $\pu{1 eV}$ to the dissociation energy of $\ce{Au2}$.6 Presumably, the effect in $\ce{Hg2^2+}$ is of a similar significance.



References


Frenking, G.; Bickelhaupt, F. M. The EDA Perspective of Chemical Bonding. In The Chemical Bond: Fundamental Aspects of Chemical Bonding; Frenking, G., Shaik, S., Eds.; Wiley: Weinheim, Germany, 2014; p 128.
Velasco, R.; Ottinger, Ch.; Zare, R. N. Dissociation Energy of Li2 from Laser‐Excited Fluorescence. J. Chem. Phys. 1969, 51 (12), 5522–5532. DOI: 10.1063/1.1671979. Free version provided by the Zare group here.
Jones, K. M.; Maleki, S.; Bize, S.; Lett, P. D.; Williams, C. J.; Richling, H.; Knöckel, H.; Tiemann, E.; Wang, H.; Gould, P. L.; Stwalley, W. C. Direct measurement of the ground-state dissociation energy of Na2. Phys. Rev. A 54, R1006(R). DOI: 10.1103/PhysRevA.54.R1006.
Weller, M.; Overton, T.; Rourke, J.; Armstrong, F. Inorganic Chemistry, 6th ed; Oxford UP: Oxford, U.K., 2014; pp 836–7.
Pyykko, P.; Desclaux, J. P. Relativity and the periodic system of elements. Acc. Chem. Res. 1979, 12 (8), 276–281. DOI: 10.1021/ar50140a002.
Pitzer, K. S. Relativistic effects on chemical properties. Acc. Chem. Res. 1979, 12 (8), 271–276. DOI: 10.1021/ar50140a001.