Last summer, I used to ride from near Porter Square to my mom's house in Weymouth all the time. The shortest way for me to go was Mass Ave, to Dorchester Ave, to Neponset Ave, and over the river onto Hancock St. The traffic on Mass Ave could be bad sometimes. Dorchester Ave does not have a lot of space for cyclists, but the flow of traffic was usually just the right speed so that I could ride right in the middle of the road with the cars. The worst part was crossing the Neponset river on that bridge. It is quite long and cars go very fast. Also, I think there is construction currently taking place somewhere on the Neponset river, so you should probably look into that. Sometimes I would go further west and cross on Adams St into Milton where the bridge is much shorter, but that route was longer and there is also a big hill after the bridge on the Milton side. Anyway, good luck.