Building on NetWallah’s approach, and adding logic to handle the pre-defined limit:

#! perl
use strict;
use warnings;
use constant LIMIT => 2;

my %cats;

while (<DATA>)
{
    my ($value, $key) = split;
    push @{ $cats{$key} }, $value;
}

for my $key (sort keys %cats)
{
    my @vals = @{ $cats{$key} };

    while (@vals)
    {
        print $key;
        my $count = 0;

        while (@vals && ++$count <= LIMIT)
        {
            print ' ', shift @vals;
        }

        print "\n";
    }
}

__DATA__
 1 cat1
 2 cat1
 3 cat2
 4 cat3
 5 cat3
 6 cat1
 7 cat1
[download]

Output:

12:58 >perl 1565_SoPW.pl
cat1 1 2
cat1 6 7
cat2 3
cat3 4 5

12:58 >
[download]

Hope that helps,