There was a similar accident here in Dominica in January - a French PA28-161 - loaded with four people on a day trip from Guadeloupe - departed just after dark - never got to the 1,500ft reporting altitude - crashed just north of the island shortly after take off - all four onboard (IR pilot, another private pilot, the other pilots's wife and teenage son) perished, bodies were never found - parts of wreckage were found the next day (main part a spar with u/c leg and tire that caused it to float to the surface). There was no mayday from the accident airplane, so it happened very fast.
In this accident it seemed likely to me that loading was likely a problem OK in daylight but at night marginal on power, at low altitude (below 1,000ft seemed likely) that even a small distraction led to the problem.
Dominica has reacted (end March 2020) by the issue of a permanent NOTAM banning night VFR departures from both of Dominica's airports. I understand that it was a night VFR departure for the short flight to TFFR - in this case it is unlikely that this reaction (if indeed it is the reason, the reason given on the NOTAM is not credible) would not have had any benefit in this case as the appropriately certified pilot would have probably have departed IFR.
I mention this here as it struck me as a PA28-181 pilot who flies out of Canefield (TDCF) that even in day I do not fully load my airplane, I have the 181 simply because of the issue of a loss of power - being overloaded or even close with an engine maybe down a little on power is big risk.