I'm a native English speaker and lifelong tea-drinker, and I have never heard of the term "husband's tea" used to mean weak tea. I did an internet search and found one very obscure and not very reliable source giving this interpretation. I think that this means what it says - a cup of tea belonging to or made for somebody's husband. One other thing that's worth pointing out...In many parts of the British Isles, especially in more traditional working-class communities, the word 'tea' is used to refer to the evening meal. So if a woman in Yorkshire, for example, says that she needs to go home to make her husband's tea, this means that she is going to make dinner for him. If you can give some more context, we'll be able to give you a better answer.

Husband's tea is a very weak, watery tea. I never take tea with Emily. She always makes husband's tea PS: or it can be simply tea of someone's husband =)