Yes, when you forget half the rule, you will find a lot of exceptions. Use the full rule and you’ll have a lot less (though still a lot of them): “I before E except after C or when sounded as A as in ‘neighbor’ or ‘weigh’”. So “weight” isn’t an exception; it’s pronounced exactly as “ei” is supposed to be pronounced. But it doesn’t take an Einstein to see that “weird” is still weird.
There’s also when the word is derived from a word that is pronounced with a long A sound, then it’s ei. For example foreign, which is related to reign (pronounced with a long A). Other exceptions are when the E and I are in two different syllables, such as science or when the word is a fairly recent borrowing from German (e.g. Fahrenheit) where it follows the German rules. None of these apply to weird, and I can’t remember off-hand why that one is an exception, but there’s a reason somewhere. The thing is, there’s so many exceptions and reasons for them, you may as well just try to memorize the words and not worry about any rules.
I always found that exception easy to remember:
I before E … except after C … and in certain weird words.
I did some greps of my thesis years ago. Indeed, there were more exceptions to the “full” rule than there were non-exceptions.
It is utter nonsense and the claim that it is a rule at all has to be stopped.
I would argue that ‘satnav’ is on its way into standard dictionaries and will soon be playable in Scrabble.