BTDT! My DS was like that from just a few months old. Being held all the time wasn't enough. If he wasn't nursing or sleeping, he wanted me to be on my feet, and he was only happy in one position...upright w/ his head on my chest/shoulder. And he'd only consent to being in the baby carrier or sling if we went outside on a walk--never inside the house. Did my posture suffer? Yes, but I was willing and able. I remember spending a lot of time staring out our living room picture window, watching squirrels and the wind in the trees.
He started walking at 10 months, so then he wanted to be moving on his own. But as soon as he got tired of using his legs, he'd want me to walk/pace with him. That was also the only way to get him to sleep most of the time, so I had plenty of time to build up my muscles. Did I get tired? Yes. I'd try shifting him around, but he still preferred just one position.
Around 18 months he started spending a little more time playing, out of my arms, but with me right there on the floor next to him. Gradually he spent more time out of my arms, but I still spent a huge portion of my days holding him (we moved, and spent about 7 months highly stressed out, so I wasn't sure how much was just his personality and how much was a reaction to parental stress). After we moved into our new-to-us house when he was almost 2.5 years old, he suddenly spent a lot longer out of my arms and playing independently.
I'd hold him while we watched movies, I'd hold him when he was calm or upset, I'd hold him to walk him to sleep for his nap and at night...it added up to hours a day. Sometimes my back did bother me, in which case I'd sit down; he'd protest; I'd explain I needed to stretch out my back/take a break; after a few minutes I'd stand back up and keep walking him back and forth.
When he dropped his nap around 3.5 years, I stopped having to walk him so much. Also, when he started sleeping through the night, that decreased the amount of time he spent in my arms, too (not that long after he dropped his nap). Now, at 4.5 years, I only hold him for about 5 minutes in the morning while we wave bye to DH as he leaves for work, and for about 5 minutes at night to get him sleepy. At around 50 pounds, he's too heavy and too big to be comfortable with my walking him to sleep anymore.
I actually want to get back into regular weightlifting just so he doesn't seem so heavy to me. =)
My suggestions for you would be to try out different baby carriers/slings to find out if your DS would be okay with any of them. Also, you could try disguising your taking a break as a chance to play some finger games/sing songs/read/ do anything else sitting down instead. I managed to get my DS used to the idea that I had to put him down when it was time for me to eat and shower.
Whatever you decide to do, as long as you're consistent about it, your DS will probably adapt. It won't be a tear-free process, but as long as you do the same thing/follow the same rule every time, your DS will eventually learn the new routine.