Weight isn't nearly as important as body structure.
You're having trouble finding anything that lists what a BP should weigh at certain ages because it doesn't really exist. There are just far too many variables. Hatchlings hatch at different weights, some start eating earlier than others, different size prey is offered in different situations, genetics are at play, etc...etc...etc...
Just like humans, some are just bigger than others, some grow faster. They're not cookie-cutter animals that are one-size-fits-all.
The main reason to track weight is being able to tell if the animal is losing weight when inevitable food strikes occur.
For example, if "snake A" weighs 1000 grams on Jan 1st and stops eating for 3 months, but only loses 50 grams it's no big deal, 5% weight loss is nothing. It can be attributed to a food strike and lack of caloric intake.
While if "snake B" weighs 1000 grams on Jan 1st and stops eating for 3 months, but loses 200 grams, which is 20% weight loss, then something may be wrong ineternally and it may be time for a vet visit. If we have accurate records it can help a vet reach a diagnosis more easily than if they're going in blind.
As for a scale, yes a kitchen scale will be fine. I g8t mine for about $20 at Wal-Mart.