The true diagonal contains contacts between loci separated by distances below the size of a bin. The 2nd diagonal has such contacts too, i.e. contacts between pairs of loci located close to the bin boundary, but on the either side of it.
Our lab's usual recommendation is to discard two first diagonals, b/c they are contaminated by non-informative artifacts of the Hi-C procedure: unligated and self-ligated molecules. The former are just pieces of undigested and unligated DNA; the latter are formed when two ends of the same molecule get ligated and then the formed circle gets cleaved elsewhere. Both types of molecules looks like short distance contacts. Unligated DNA pieces look like two contacts with a separation of a few hundred bp and with the sequencing directions pointing toward each other along the genome. Self-ligated molecules usually have a separation of a few kb to 10 kb and have sequencing directions pointing away from each other. Both do not contain information about spatial organization. B/c unligated DNA and self-circles cannot be distinguished from "true" contacts formed by two distinct ligated molecules, their presence essentially invalidates all statistics on short-distance contacts. For this reason, we usually discard the first two diagonals of Hi-C matrices at high resolutions (up to a few tens of kb) or only the first diagonal for low resolution datasets (100kb+).
What's the size of the bins in you matrix? Let's say the bins are 5kb long. The values in the diagonal means that you see interactions at very short distance (less than 5kb). To me these values should be the highest values.
So you are estimating contacts between fragments. But obviously, fragments which are already very close together (i.e. in the same bin) are highly likely in close proximity with each other. And that's not exactly what you are looking for, probably.
You probably want to check for secondary structure interactions such as looping, not for interactions because of the primary sequence - proximity.