Using sqlite (and most likely any other SQL database) you can convert your wide data to long data and then find the most common value.
SELECT value FROM
(
SELECT 'Week1' AS week, week1 AS value FROM 'weeks'
UNION ALL
SELECT 'Week2' AS week, week2 AS value FROM 'weeks'
UNION ALL
SELECT 'Week3' AS week, week3 AS value FROM 'weeks'
UNION ALL
SELECT 'Week4' AS week, week4 AS value FROM 'weeks'
)
GROUP BY value
ORDER BY count(*) DESC
LIMIT 1;
Add more columns as necessary and maybe a where clause for filtering by year.
Since SQL doesn't natively support column wildcards you might consider converting your data from wide to long as others have pointed out in the comments.
Relevant posts:
Mode in sqlite: Calculating the mode with SQLite with grouping
Wide to long in sql (hive): Convert data from wide format to long format in SQL