Over the past couple of months one of my clients started noticing backups were taking a long time and the size of the resulting backups was becoming an issue. To help identify exceptionally large tables I made use of MySQL's INFORMATION_SCHEMA feature and the following query worked very well.
SELECT count(*) tables,
concat(round(sum(table_rows)/1000000,2),'M') rows,
concat(round(sum(data_length)/(1024*1024*1024),2),'G') data,
concat(round(sum(index_length)/(1024*1024*1024),2),'G') idx,
concat(round(sum(data_length+index_length)/(1024*1024*1024),2),'G') total_size,
round(sum(index_length)/sum(data_length),2) idxfrac
FROM information_schema.TABLES
WHERE table_schema = 'database-name'
ORDER BY data_length+index_length DESC LIMIT 10;