The fact that many people have babies/children who don't sleep until they are 18 months or 2 or 3 or even 6, and who clearly weigh a good deal by then, does not mean sleeping through has nothing to do with weight.
There are many reasons why these babies/children wake at night. It could be hunger,due to not getting all of their calorie needs for 24 hours during waking hours, it could be because they cannot self settle after waking, it could be due to habit ....or loads of other reasons I can't think of.
However, there IS a relationship between weight and when a young baby can sleep through. Before they can sleep through, their tummy needs to be able to hold enough food for them to sleep longer without needing to feed again to fill it up,due to tiny size. This does not often occur before a baby is 10 to 12lb.
This does not mean that even baby who reaches this weight will sleep through. As mentioned above there are numerous other reasons which might mean they don't, but beyond this point, it is unlikely to be weight keeping them awake, but UNTIL this point, weight WILL be a key factor.
The OP is enquiring about her young baby and wondering when is the earliest she can possibly expect him to sleep through in terms of weight, hoping the other factors which might delay sleeping through are not there. Of course those other factors might be there, but they might not be. Therefore, I would say that one baby reaches 10lb or so it becomes possible to sleep through, but not inevitable by any means.
The fact that many of your children weighed several stones before they slept through, does not mean it is totally unrelated to weight for small babies.