I rearranged your structure a little bit, for clarity, and you are awfully close to sorting it. For example:

#!/usr/bin/perl -w
use strict;

my @array = ( { name => "proteobacteriai", 
                size => 30 },
              { phylum => "alphabacteria",  
                size => 50 },
              { name => "cytophaga",   
                size => 10 },
);
for (@array) {
    print "Size (out of order) = ",$_->{size}, "\n";
}

my @newarray = sort { $a->{size} <=> $b->{size} } @array;

for (@newarray) {
    print "Size = ",$_->{size}, "\n";
}
[download]

yields

C:\Code>perl sort_aoh.pl
Size (out of order) = 30
Size (out of order) = 50
Size (out of order) = 10
size = 10
size = 30
size = 50
[download]