Número total de registros por semana

1. 
   O desempenho de um CROSS JOIN incondicional deteriora-se rapidamente com o número crescente de linhas. O número total de linhas é multiplicado pelo número de semanas que você está testando, antes que essa enorme tabela derivada possa ser processada na agregação. Os índices não podem ajudar.
   
2. 
   Começar semanas com 1º de janeiro leva a inconsistências. semanas ISO pode ser uma alternativa. Veja abaixo.
   

Junte-se apenas a linhas relevantes

SELECT d.day, d.thisyr
     , count(t.exam_date) AS lastyr
FROM  (
   SELECT d.day::date, (d.day - '1 year'::interval)::date AS day0  -- for 2nd join
        , count(t.exam_date) AS thisyr
   FROM   generate_series('2013-01-01'::date
                        , '2013-01-31'::date  -- last week overlaps with Feb.
                        , '7 days'::interval) d(day)  -- returns timestamp
   LEFT   JOIN tbl t ON t.exam_date >= d.day::date
                    AND t.exam_date <  d.day::date + 7
   GROUP  BY d.day
   ) d
LEFT   JOIN tbl t ON t.exam_date >= d.day0      -- repeat with last year
                 AND t.exam_date <  d.day0 + 7
GROUP  BY d.day, d.thisyr
ORDER  BY d.day;

O mesmo com semanas ISO

SELECT w AS isoweek
     , day::text  AS thisyr_monday, thisyr_ct
     , day0::text AS lastyr_monday, count(t.exam_date) AS lastyr_ct
FROM  (
   SELECT w, day
        , date_trunc('week', '2012-01-04'::date)::date + 7 * w AS day0
        , count(t.exam_date) AS thisyr_ct
   FROM  (
      SELECT w
           , date_trunc('week', '2013-01-04'::date)::date + 7 * w AS day
      FROM   generate_series(0, 4) w
      ) d
   LEFT   JOIN tbl t ON t.exam_date >= d.day
                    AND t.exam_date <  d.day + 7
   GROUP  BY d.w, d.day
   ) d
LEFT   JOIN tbl t ON t.exam_date >= d.day0     -- repeat with last year
                 AND t.exam_date <  d.day0 + 7
GROUP  BY d.w, d.day, d.day0, d.thisyr_ct
ORDER  BY d.w, d.day;

date_trunc('week', '2012-01-04'::date)::date

Simplifique com EXTRACT()

SELECT w AS isoweek
     , COALESCE(thisyr_ct, 0) AS thisyr_ct
     , COALESCE(lastyr_ct, 0) AS lastyr_ct
FROM   generate_series(1, 5) w
LEFT   JOIN (
   SELECT EXTRACT(week FROM exam_date)::int AS w, count(*) AS thisyr_ct
   FROM   tbl
   WHERE  EXTRACT(isoyear FROM exam_date)::int = 2013
   GROUP  BY 1
   ) t13  USING (w)
LEFT   JOIN (
   SELECT EXTRACT(week FROM exam_date)::int AS w, count(*) AS lastyr_ct
   FROM   tbl
   WHERE  EXTRACT(isoyear FROM exam_date)::int = 2012
   GROUP  BY 1
   ) t12  USING (w);

Consulta otimizada

WITH params AS (          -- enter parameters here, once 
   SELECT date_trunc('week', '2012-01-04'::date)::date AS last_start
        , date_trunc('week', '2013-01-04'::date)::date AS this_start
        , date_trunc('week', '2014-01-04'::date)::date AS next_start
        , 1 AS week_1
        , 5 AS week_n     -- show weeks 1 - 5
   )
SELECT w.w AS isoweek
     , p.this_start + 7 * (w - 1) AS thisyr_monday
     , COALESCE(t13.ct, 0) AS thisyr_ct
     , p.last_start + 7 * (w - 1) AS lastyr_monday
     , COALESCE(t12.ct, 0) AS lastyr_ct
FROM params p
   , generate_series(p.week_1, p.week_n) w(w)
LEFT   JOIN (
   SELECT EXTRACT(week FROM t.exam_date)::int AS w, count(*) AS ct
   FROM   tbl t, params p
   WHERE  t.exam_date >= p.this_start      -- only relevant dates
   AND    t.exam_date <  p.this_start + 7 * (p.week_n - p.week_1 + 1)::int
-- AND    t.exam_date <  p.next_start      -- don't cross over into next year
   GROUP  BY 1
   ) t13  USING (w)
LEFT   JOIN (                              -- same for last year
   SELECT EXTRACT(week FROM t.exam_date)::int AS w, count(*) AS ct
   FROM   tbl t, params p
   WHERE  t.exam_date >= p.last_start
   AND    t.exam_date <  p.last_start + 7 * (p.week_n - p.week_1 + 1)::int
-- AND    t.exam_date <  p.this_start
   GROUP  BY 1
   ) t12  USING (w);