The following seems to do what you want using a simple linear interpolation. The trick is figuring out which two data points to interpolate between. That's what the shift @rawData while ... is doing.

use strict;
use warnings;
use POSIX;

use constant kIntervals => 10.0;

my @rawData;
my $tmin;
my $tmax;
my $secPerDay = 60 * 60 * 24;

for (<DATA>) {
    chomp;
    next unless m{^\s*([\d/]+)\s+([\d.]+)};
    
    my ($m, $d, $y) = split /\//, $1;
    my $weight = $2;
    my $date = POSIX::mktime(0, 0, 0, $d, $m - 1, $y - 1900);

    $tmin = $date if ! $tmin;
    $date -= $tmin;
    $tmax = $date /= $secPerDay;
    push @rawData, [$date, $weight];
}

my ($wmax, $wmin) = ($rawData[0][1], $rawData[-1][1]);
my $interval = $tmax / kIntervals;
my $wcalc = $wmax;
my $wgone;
my @data;

for my $point (0 .. kIntervals) {
    my $epoch = $point * $interval;
    
    shift @rawData while @rawData > 1 && $rawData[1][0] < $epoch;
    last if ! @rawData;
    
    if (@rawData == 1) {
        push @data, [$epoch, $rawData[0][1]];
        last;
    }

    my $m = $rawData[0][1];
    my $s = ($rawData[1][1] - $rawData[0][1]) / ($rawData[1][0] - $raw
+Data[0][0]);
    
    push @data, [$epoch, $m + $s * ($epoch - $rawData[0][0])];
}

printf "%d\t%5.1f\n", $_->[0], $_->[1] for @data;

__DATA__
6/26/2010 334
8/12/2010 311.8
8/19/2010 308.4
9/5/2010 300.0
9/9/2010 298.6
9/14/2010 297.2
9/16/2010 293.6
[download]

Prints:

0    334.0
8    330.1
16    326.3
24    322.4
32    318.5
41    314.6
49    310.7
57    306.7
65    302.7
73    299.0
82    293.6
[download]

I haven't bothered with the graphing code, mostly because that makes it harder to compare results without posting a graph.

Note that the %s strftime format code is non-standard. I used mktime instead to get epoch seconds then converted that into delta days.

Update: Fixed interval calculation bug - use $interval instead of kIntervals!