Why is the first member of group IVA and the second member of group VIA show stronger tendencies to catenate compared to the other group members?
The ability to catenate appears to be based on several factors:


The bond energy of the element to itself - stronger bonds promote catenation
Atom size - smaller atoms promote catenation due to lower steric demand and better orbital overlap (especially p-p)
Degree to which orbital hybridization is important in the structure of that elements compounds (for example, the bond angle in $\ce{NH3}$ is $\sim 108^\circ$ while that of $\ce{AsH3}$ is more like $90^\circ$
Electronegativity of that element - atoms with electronegativity in the middle of the scale appear to catenate best.


Here is a plot of bond energy and electronegativity for the first 36 elements. Note that there appears to be a sweet spot of electronegtaivity between ~2 and ~3 that produces high bond energies. In the box I drew are all of the elements that are known to have covalent compounds containing more than 3 catenated atoms of that element. In case you were wondering, I used bond energies for single bonds only so comparison was better.



Note that hydrogen is in this box. Hydrogen cannot catenate since it has only one valence electron, but if it had electrons in the second shell, it probably would catenate.