Replace

    if(('$checkvalue' gt '$value1') &&
       ('$checkvalue' le '$value2'))
    {
        print "$checkvalue $value1 $value2\n";

    }
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with

    if(($checkvalue > $value1) &&
       ($checkvalue <= $value2))
    {
        print "$checkvalue $value1 $value2\n";

    }
[download]

gt and le are string-wise comparisons. > and <= are numeric comparisons.

Update: As VSarkiss (below) and Aviator (in /msg) have correctly pointed out, the bigger issue wasn't that the OP was using the string-wise comparisons (though that was still a problem), but that the OP was comparing the variable names, not that variable values - due to the single-quotes.