How can I find a module or activity that is excessively writing to the database? Problem:

We have two productions servers: primary and failover. The two machines are linked via mysql replication. The mysql relay logs are clogging and bringing servers down the failover server. I see dozens of mysqld-relay-bin.000Xxxx files in /var/lib/mysql on the failover box.  

My Question: 

How might I find if a module or some other activity is doing excessive database writes?

Why am I asking a sql question on DA?

Now I'm asking this in Drupal Answers because we're trying to trace this from source to destination. I have a suspicion that we have a module that is a bit over-aggressive at logging. We only have two content editors and changes are made on a few pages a day. I've also asked a similar question on https://superuser.com/questions/869776/ to see if there is a more mysql-specific remedy.

Master my.cnf

$ cat /etc/my.cnf 
[mysqld]
datadir=/var/lib/mysql
socket=/var/lib/mysql/mysql.sock
user=mysql
# Disabling symbolic-links is recommended to prevent assorted security risks
symbolic-links=0

# sync
log-bin=mysql-bin
server-id=1
expire_logs_days = 1
max_binlog_size  = 100M
.
.
.
# sync config
log-bin = /var/log/mysql/mysql-bin.log
binlog_do_db=drupal
server-id=1 


Replicant (Slave) my.cnf

$ cat /etc/my.cnf
[mysqld]
datadir=/var/lib/mysql
socket=/var/lib/mysql/mysql.sock
user=mysql
# Disabling symbolic-links is recommended to prevent assorted security risks
symbolic-links=0

server-id=2
master-host=xxx.xx.xx.xxx
master-user=slave_user
master-password=XXXXXXXXXXXXXXX
master-connect-retry=60
replicate-do-db=drupal
slave-skip-errors = 1062,1054
expire_logs_days = 2
max_binlog_size  = 100M
ssl


Various or interesting finds in the logfile via tail -n 10000 messages | grep drupal | grep -v "page not found"  | grep -v "access denied"

Warning: in_array() expects parameter 2 to be array, string given in context_menu_tree_add_active_path() (line 128 of /var/www/html/sites/all/modules/context_menu_block/context_menu_block.module).


Other considerations:


Drush runs once an hour via the OS's crontab. We pull in multiple calendar and RSS feeds to keep updated content. 
We've recently migrated this site to Drupal. Our log files still indicate a few broken, dead links that spiders are finding. Which if I had db_log/watchdog enabled would be an obvious culprit.
I recommend turning on mysql query log and examining types of queries flooding your server.

Or, pay for a product like New Relic or AppDynamics which provide per-url PHP performance metrics (including DB usage) of your application on web servers.