I agree your body is just resting up for birth. If it feels like you're too tired though you can have your doc test your iron levels. Low iron will make you extremely tired too but it's a very easy fix.
Yes, it's completely normal. I'm 35 weeks also and I'm so tired, I feel like I don't have any energy to wash dishes or anything. But both ladies above are right. Rest up because your going to miss these days when the baby comes lol.
I agree with mamagris just take your time because once the baby gets here you will miss the rest lol but I missed my belly once I had my daughter so im making sure with my son I just sit bck and enjoy it...but at bed time its a whole other story :/
Maybe because you were on the go so much before it is your bodies way of catching up. Rest is good too! Enjoy the time with your belly being big and wiggling. Oddly enough you miss it when its gone (or I am wierd and did anyway)