Your two-query approach is often acceptable. However, if you want to combine them into one statement, try something like:

# Assumes the time is coming in as 12:47:02
sub get_pressure
{
    my ($data_time) = @_;

    my $sql = <<__END_SQL__;
SELECT weather_time
      ,baro_pressure
  FROM pressure
 WHERE weather_time < TO_DATE(?, 'HH:MI:SS')
 ORDER BY weather_time DESC
__END_SQL__

    my $sth = $dbh->prepare($sql) || die ...
    $sth->execute($data_time)     || die ...

    $sth->bind_columns(\my ($press_time, $pressure));

    # You only want the first column returned.
    $sth->fetch;

    return $pressure;
}
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(Note the use of placeholders ...)

You're looking for the largest weather_time, so you can just order them descending.

I'm not fully up on DBI::AnyData's restrictions. Personally, I would have used DBD::SQL_Lite and taken the overhead of the schema definition. *shrugs*