I don't know about the legs feeling like weights or about how slow you walk but....
YAY YOU!!!! Starting a walking plan is awesome! Do what you can, you have to build up your stamina and let your body get used to it.
When i started out, I couldn't walk 3 house lengths on my street. Now I can lap my mile round street like nobody's business! There are still days that I can't do it for whatever reason so I walk shorter lengths multiple times so the walk home isn't far if I have to stop sooner than later.
I'm so happy for you, this is a big step in your plan (no pun intended!)!!