This is a Perl forum, but I generated your graph in less than a minute with Excel. File|Open import data using space delimiter, select data, graph as a line graph (connect each data point with a straight line). I will point out that it is certainly not "cheating" to have Perl drive the Excel program to automate the above! But of course that will take longer than one minute to code. Another technique is to make an Excel macro and have Perl drive that macro command rather than the details of it.

BTW, your progress is amazing! And very consistent! Great!

To do this yourself, I would convert date/time to say epoch time. calculate min,max of X and Y scale. Then decide how many "buckets" you will have in each direction. Place each data point to closest X,Y coordinate that your scaling system allows. Calculate intermediate y points along the x axis between 2 points with y=mx+b. A line graph is better here than a bar.

Your data is so consistent that I don't see any need, but in some cases you would want to make a single line that represents the "best fit" of all the data points. One technique is least squares approximation. There is a way to get Excel and other spreadsheet programs to do that.

Update:
Oh, I see that this is some CGI thing. Ok, some code that shows a bit of a different way is below..hope it helps..

#!/usr/bin/perl -w
use strict;
use Time::Local;
use Data::Dumper;

my @data;
my @graph;
my $one_day = 60*60*24;    #one day in seconds

while (<DATA>)
{
   next if /^\s*$/;                #skip blank lines
   my ($date, $weight) = split;
   my $epoch = epoch($date);
   push (@data, [$epoch, $weight]);
}

# input data is sorted already sorted
# But the algortihm depends upon sorted date information
# so I did that to make sure
#
  @data = sort{$a->[0] <=> $b->[0]} @data; 
                                          
# axis x will be adjusted to #days from the date of first data
# axis y is in weight  

my ($x_base_epoch, $y1) = @{shift(@data)};
my $x1_day =0;
                                            
foreach my $r_xy(@data)
{
   my ($x2, $y2) = @$r_xy;
   $x2 -= $x_base_epoch;
   my $x2_day = int($x2/$one_day);
     
   # slope is delta weight/ delta days
     my $slope = ($y2-$y1)/($x2_day-$x1_day); 
   
   # fill in missing data points...
   # by linear interpolation 
   
   for (; $x1_day< $x2_day; $x1_day++) # x interval not tested for
                                       # other than 1
   {
      my $y = $slope*($x1_day-$x2_day) + $y2;
      push @graph, [$x1_day,$y];
   }   
         
   $y1= $y2;
}

#fix-up for last data point
my ($fx,$fy) = @{$data[-1]};
push @graph, [($fx-$x_base_epoch)/$one_day, $fy];

### data to graph is in @graph  ###
### I leave that part to the OP ###
print "$_->[0] $_->[1]\n" foreach @graph;

sub epoch
{
   my $date = shift;
   my ($month, $day, $year) = split(m|/|,$date);
   my $time = timelocal(0,0,0, $day, $month-1, $year-1900); 
   return $time;
}

=prints
0 334
1 333.527659574468
2 333.055319148936
3 332.582978723404
4 332.110638297872
.....
74 298.95
75 298.6
76 298.32
77 298.04
78 297.76
79 297.48
80 297.2
81 295.4
82 293.6
=cut

__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]

Update to Update:

Using a different x axis increment than "one" can get to problematic depending upon what you are trying to do. Often one would want to show the actual data points with some special character and the points inbetween with another character. So if you just want to show say weekly progress, then you have to decide what that would mean in terms of the graphical representation - eg the "weekly Monday point" may not represent any factual point at all. Generating the "weight" for each day is very efficient. If you want something like a "Monday" value it would not be ridiculous to generate all points in the week or year and then just print every 7th value.