For some reason, on every character I play as, I just cannot give my children in Hearthfire a gift. They'll ask if I got them a gift, and I'll say yes (because I have a doll/dress/wooden sword in my pocket) and then it opens the menu for me to give them stuff. However, whenever I do this, a text appears saying "This item is too heavy to carry" and I can't give them it. What do I do? And why is it doing this...? HELP!

Is the child Sofie?

On one playthrough :/ But this is on ALL of my playthroughs, and every one has different children.

Hmmm I dont know about the others, but apparently Sofie is bugged, because even though she's not official, she is a merchant in that she sells her flowers. And for some reason that messes up the ability to give her gifts. Not sure about the other kids.

Maybe try uninstalling then re-installing Hearthfire?