Kim,
I have the PRTS transcript of Heathfield registers. It says for burials in 1698 (and several years around that time) only the BT entries are available.
The HARMER entries in 1698 are:
1 June buried Mary HARMAR
18 June buried William HARMAR
No age or relationship information is given, but around that time it often was. For example, the entry before that of William records the burial of "Sarah the wife of John NORDEN" on 4 June. This doesn't give confidence in the entry for Mary HARMER being that of William's wife.
There is no entry for the 3 January, even after allowing for the old style calendar.