Evidence Against Robin
There is really no evidence against Robin, however, there were a number of items which formed the basis of 'new evidence' that supposedly exonerate David by incriminating his father. Essentially little of it was new evidence, but mostly it involved reinterpretations of old evidence and claims that mistakes made in the first trial may have resulted in the jury being unintentionally misled.
The items brought to the Privy Council can be viewed at Wikipedia and are categorized on this site as either Against Robin or Conflicting.
A witness described Robin as becoming increasingly depressed prior to the killings.
The allegation that Robin had an incestual relationship with Laniet and that this provides motive for murder.