If I'm not mistaken, that should be:
$dbcnx = @mysql_connect( "mysql.jodoshared.com",<myuserID>,<mypwd>) or die ('I cannot connect to the database because: ' . mysql_error());
mysql_select_db("DaveC42_weight_test",$dbcnx);
$result = mysql_query("SELECT * FROM weight_data")...