It has been growing but vary little. I have a seperate /var filesystem at root level, but as shown in the ls -l below of /usr, there is a /usr/var also.
USFYDB01.dakamericas.com-oracle> ls -l
total 12062
drwxr-xr-x 4 root system 8192 Nov 19 1996 OV
-rw-r--r-- 1 root system 3049 Feb 3 1997 USFYDB01.save
-rw-r--r-- 1 root system 3049 Feb 4 1997 USFYDB01.save2
lrwxrwxrwx 1 root system 10 Jun 5 1999 adm -> ../var/adm
drwxr-xr-x 2 root system 8192 Nov 19 1996 advfs
drwxr-xr-x 7 root system 16384 Jun 5 1999 bin
drwxr-xr-x 4 root system 8192 Nov 13 1998 ccs
lrwxrwxrwx 1 root system 12 Jun 5 1999 dict -> ./share/dict
drwxr-xr-x 5 root system 8192 Jun 5 1999 doc
drwxr-xr-x 10 root system 8192 Jun 5 1999 dt
drwxr-xr-x 15 root system 8192 Jun 5 1999 examples
drwxr-xr-x 3 root system 8192 Jun 5 1999 field
drwxr-xr-x 17 root system 8192 Jun 5 1999 include
drwxr-xr-x 4 root system 8192 Jun 5 1999 lbin
drwxr-xr-x 16 root system 8192 Jun 5 1999 lib
drwxr-xr-x 3 root system 8192 Feb 7 1997 local
drwxr-xr-x 2 root system 8192 Apr 13 2001 logs
lrwxrwxrwx 1 root system 9 Jun 5 1999 man -> share/man
lrwxrwxrwx 1 root system 11 Jun 5 1999 news -> ../var/news
drwxr-xr-x 3 root system 8192 Apr 8 1998 onlinet
drwxr-xr-x 12 root system 8192 Nov 13 1998 opt
lrwxrwxrwx 1 root system 15 Jun 5 1999 preserve -> ../var/preser
ve
-rw-r----- 1 root operator 8192 Jan 29 1997 quota.group
-rw-r----- 1 root operator 286720 Jan 29 1997 quota.user
drwxr-xr-x 4 root system 16384 Jun 5 1999 sbin
drwxr-xr-x 9 root system 8192 Jun 5 1999 share
drwxr-xr-x 8 root system 8192 Aug 28 12:59 shlib
drwxr-xr-x 3 root system 8192 Jun 5 1999 skel
lrwxrwxrwx 1 root system 12 Jun 5 1999 spool -> ../var/spool
drwxr-xr-x 19 root system 8192 Nov 13 1998 sys
drwxr-xr-x 2 root system 8192 Dec 13 2000 systools
drwxr-xr-x 3 root system 8192 Nov 13 1998 tcb
lrwxrwxrwx 1 root system 10 Jun 5 1999 tmp -> ../var/tmp
lrwxrwxrwx 1 root system 5 Jun 5 1999 ucb -> ./bin
drwxr-xr-x 6 root users 8192 Aug 28 12:56 users
drwxrwxrwx 26 root system 8192 Jun 5 1999 var
-rwxr-xr-x 1 root system 12103760 Jul 31 1997 vmunix.sav
USFYDB01.dakamericas.com-oracle>