this seems to work, although not a compact, single query solution. it also only works if the duplicates are a result of 2 sources (it wouldn't select a single value if duplicate values came from sources 'A', 'B', and 'C'):

--table of just duplicates
create table dups as
select t1.*, st_centroid(st_union(t1.geom, t2.geom)) as cent_geom
from points as t1 join points as t2 on st_dwithin(t1.geom, t2.geom, 10)
where t1.date = t2.date and t1.gid != t2.gid
order by date, value desc;

--table of no duplicates
create table no_dups as select points.*
from points left join dups on points.gid = dups.gid
where dups.gid is null;

--insert distinct duplicates
insert into no_dups
select distinct on (date, cent_geom) dups.*
from dups;

select * from no_dups
order by gid;

this seems to work, although not a compact, single query solution. it also only works if the duplicates are a result of 2 sources (it wouldn't select a single value if duplicate values came from sources 'A', 'B', and 'C'):

--table of just duplicates
create table dups as
select t1.*, st_centroid(st_union(t1.geom, t2.geom)) as cent_geom
from points as t1 join points as t2 on st_dwithin(t1.geom, t2.geom, 10)
where t1.date = t2.date and t1.gid != t2.gid
order by date, value desc;

--table of no duplicates
create table no_dups as select points.*
from points left join dups on points.gid = dups.gid
where dups.gid is null;

--insert distinct duplicates
insert into no_dups
select distinct on (date, cent_geom) gid, date, source, value, geom
from dups;

select * from no_dups
order by gid;

this seems to work, although not a compact, single query solution:

--table of just duplicates
create table dups as select t1.*
from points as t1 join points as t2 on st_dwithin(t1.geom, t2.geom, 10)
where t1.date = t2.date and t1.gid != t2.gid
order by date, value desc;

--table of no duplicates
create table no_dups as select points.*
from points left join dups on points.gid = dups.gid
where dups.gid is null;

--insert distinct duplicates
insert into no_dups
select distinct on (date) dups.*
from dups;

select * from no_dups
order by gid;

this seems to work, although not a compact, single query solution. it also only works if the duplicates are a result of 2 sources (it wouldn't select a single value if duplicate values came from sources 'A', 'B', and 'C'):

--table of just duplicates
create table dups as 
select t1.*, st_centroid(st_union(t1.geom, t2.geom)) as cent_geom
from points as t1 join points as t2 on st_dwithin(t1.geom, t2.geom, 10)
where t1.date = t2.date and t1.gid != t2.gid
order by date, value desc;

--table of no duplicates
create table no_dups as select points.*
from points left join dups on points.gid = dups.gid
where dups.gid is null;

--insert distinct duplicates
insert into no_dups
select distinct on (date, cent_geom) dups.*
from dups;

select * from no_dups
order by gid;