I see no need for the while loop:

use warnings;
use strict;

undef $/;
my $content = <DATA>;

$content =~ s/<span style="font.*/<span style="font-weight: bold;">/gi
+;
print "$content\n";

__DATA__
<span style="font-weight: bold;color:#000000;">
<span style="font-family:Arial MT;font-size: 25px; font-weight: bold;"
+> 
<span style="color:#000000;" xmlns="http://www.w3.org/1999/xhtml">
[download]

prints:

<span style="font-weight: bold;">
<span style="font-weight: bold;">
<span style="color:#000000;" xmlns="http://www.w3.org/1999/xhtml">
[download]

See also:

• perldoc perlre
• HTML parse