My DD did that around 5-7 weeks of age... she will now sleep during the day in her bassinette or pram and in a variety of other places... I can't remember when she did start sleeping longer without the sling but I just remember that when I put her down she wouldn't wake immediately again.

For me I just rode the wave and figured that she would eventually figure out that the pram, bassinette etc were not the enemy. I enjoyed wearing her (and usually do when we are out) but yeah my back started to really hate me for a while there LOL.

GL hope your back gets a break soon