The car seat we bought for everyday car use for my daughters is a pretty beefy unit. It was the top rated convertible at the time, the Britax something or other. It hefted that thing once and thought "this isn't for airplanes."
So I found the lightest weight one I could, called the
Cosco Scenera Next; not
Costco like the big box store, rather the tee-less version. It is super light! And I don't feel the safety is compromised much. The thing that makes the other one heavy is the articulating base that allows cant adjustment.
You do have to face them forward even for younger toddlers, before the recommended forward facing age, but not much choice there. It's sized for toddlers, but the next step up in kid size is a booster-style seat. I haven't yet looked for lightweight versions of those yet. It has the anchor strap that you can easily run over the seatback and down to the anchor in the floor of a Cessna like Robw56 is talking about.

I'd advise no front seat for small children. Hopefully only a few of you recall the midair at Johnson Creek in 2013 where the 2 year old died from blunt force trauma. I don't remember exact specifics, but he was in the front seat and I think that was a contributing factor.