File/libmagic: What is the “ID3 length”

2-3 files per second tested with file seems very slow to me. file actually performs a number of different tests to try and determine the file type. Since you are looking for one particular type of file (sqlite), and you don't care about identifying all the others, you can experiment on a known sqlite file to determine which test actually identifies it. You can then exclude the others using the -e flag, and run against your full file set. See the man page:

 -e, --exclude testname
         Exclude the test named in testname from the list of tests made to
         determine the file type. Valid test names are:

         apptype
            EMX application type (only on EMX).
         text
            Various types of text files (this test will try to guess the
            text encoding, irrespective of the setting of the ‘encoding’
            option).
         encoding
            Different text encodings for soft magic tests.
         tokens
            Looks for known tokens inside text files.
         cdf
            Prints details of Compound Document Files.
         compress
            Checks for, and looks inside, compressed files.
         elf
            Prints ELF file details.
         soft
            Consults magic files.
         tar
            Examines tar files.

Edit: I tried some tests myself. Summary:

1. Applying my advice with the right flags can speed up file by about 15%, for tests to determine sqlite. Which is something, but not the huge improvement I expected.
2. Your file tests are really slow. I did 500 on a standard machine in the time you did 2-3. Are you on slow hardware, or checking enormous files, running an ancient version of file, or...?
3. You must keep the 'soft' test to successfully identify a file as sqlite.

For a 16MB sqlite DB file, I did:

#!/bin/bash
for  i in {1..1000}
do
    file sqllite_file.db | tail > out
done

Timing on the command line:

~/tmp$ time ./test_file_times.sh; cat out

real    0m2.424s
user    0m0.040s
sys 0m0.288s
sqllite_file.db: SQLite 3.x database

Trying the different test excludes, and assuming the determination is made based on a single test, it is the 'soft' (i.e. magic file lookup) test which identifies the file. Accordingly, I modified the file command to exclude all the other tests:

file -e apptype -e ascii -e encoding -e tokens -e cdf -e compress -e elf -e tar sqllite_file.db | tail > out

Running this 1000 times:

~/tmp$ time ./test_file_times.sh; cat out

real    0m2.119s
user    0m0.060s
sys         0m0.280s
sqllite_file.db: SQLite 3.x database

People had been writing scripts (and possibly C programs) to run file on a file, capturing the output with $(file foobar) or popen(), and doing a string match check to see whether the output from file contained (or ended with) the word “text”.  Then the developers of the Berkeley Software Distribution (at the University of California, Berkeley) did as described and caused all those scripts and programs not to recognize shell script files as text files.