Your pediatrician should be able to answer this, as it does border on asking for medical advice.
If you do a literature search, intervertebral disc herniation ("ruptured disc"), the most serious consequence of heavy lifting in adults, is considered rare in children, and is usually the result of trauma, with the youngest child on record with the problem was a two year old who fell out of a crib (Great! Yet another reason to worry about kids falling out of cribs!)
The incidence of low back pain, however, is not rare, and is actually fairly common. Various reports place it at between 17% to 48% in grammar school aged children. The American Academy of Pediatrics has placed restrictions on back-pack weight, however, the association between heavy backpacks and back pain is controversial. And while back pain in adults has been rigorously studied (partly because of its economic impact), it has only relatively recently been studied in children, maybe because there is little economic impact, the mistaken impression that it is only caused by serious disease in children, or the impression that children's backs are not as likely to be injured as those of adults. However, like adults, sedentary lifestyle (e.g. lots of TV) does increase the likelihood of back strain in children, and kids with low back pain are more likely to have chronic back pain as adults.
The bottom line? I couldn't find a good study of the impact of lifting on children's backs. So I would suggest asking a pediatrician, the person most familiar with back pain and it's causes/prevention in children.
There are reasons why some issues have been much studied and not others; a good example is how very little research there was on cardiovascular disease in women as opposed to men until relatively recently. (You can probably deduce the reason yourself.) I think most people would think it is not a problem out of lack of information otherwise, just as 30 years ago, there was a belief that CVD wasn't a problem in women.
Edited to add: I can't recall seeing a child in my practice or the ER who presented with musculoskeletal back pain, the kind you're concerned about. (I did see kids with back pain of other etiologies.) It might be that I did see some but wouldn't remember it. So my experience would have predisposed me to say "It's not a problem." I mean, kids pick up their siblings all the time and I don't recall seeing an injury. Having said that, my thinking was changed by the papers on pediatric back pain that I found. So if this sounds unduly alarming, that's the reason.
There's a more recent version of this paper on back pain in children, but it's behind a paywall.