I do something similar but its a pic 16f877 i read from that polls Dallas One-wire 18s20 temp sensors. i use the following

$ob->read_char_time(5);            # avg time between read char
$ob->read_const_time(500);         # timeout after 500 milliseconds = 
+0.5 seconds
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I also am looking for complete lines so i use

my $ob = tie (*FH, 'Device::SerialPort', $cfgfile)
       || die "Can't tie: $!\n";             ## TIEHANDLE ##
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and to read in all available lines i use

    @gotits=<FH> ;
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This seems to work well for me, but i can get a bunch of lines all at once for while i too only cycle every 15 seconds a cycle reads about 50 18s20 sensors 6 at a time and there may not be much time between the lines for each sensor.

One thing that may be affecting you is that

$timestamp = uts_to_iso(time());
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runs even if you do not want to insert the lines.

Another thing i noticed is repeated calls to dt(). saying

my $dtdate=dt('date'); my $dttime=dt('time');
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and then using the variables in the execute may speed things up.

and a last observation is that each insert cycle you run the $dbh->prepare($q); pulling these out of the while loop such that

$q = "insert into weather_data values (?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?
+, ?, ?, ?, ?, ?, ?)";
my $sth = $dbh->prepare($q);
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is only run once, nd the loop code just uses $sth->execute(...); may speed things up a whole lot.