I would not recommend Weymouth at all to be honest with you Especially with Children, Unfortunately Weymouth has gone Downhill fast..There is a huge Drug problem here and it is only getting worse, It wont matter what Side of Weymouth you live on as that will not help you with the school problem which is well known to be a mess, I currently live in Weymouth and was advised get out before I was forced to send my kid to the schools and thats exactly what I'm going to do
I now hear Weymouth being referred to as Brockmouth or Brockton by the bay..
Check GreatSchools.org and that will help you to evaluate a towns school system..Weymouth used to be a really nice town to live but has been over run by drugs..Best Wishes to you and your family I hope everything works out