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There are two clues I am uncertain about,

1. How does one parse this clue with what I think is the word BALANCED?

Level headed daughter follow what's left (8)

2. This one has me stumped.

Little weight of publication explained initually by reference to quality of paper (8)

The letters I am certain of: ?R?M?A?E based on the ACROSS clues. This one is a DOWn clue.

CRIMAGE has been suggested, but it is difficult to parse it. So has KRUMKAKE.

Any suggestions from anyone?

The balance is the money left over when something has been settled.

GRAMMAGE - poor clue as GRAM has the same meaning in wordplay and answer

Missed part of the explanation:
GRAM - little weight
MAG - publication
E(xplained)

Oh, and it's a measure of the quality of paper:

https://en.wikipedia.org/wiki/Grammage#:~:text=Grammage%20and%20basis%20weight%2C%20in,of%20its%20thickness%20(caliper).

Thank you very help for the help.

Never have been disappointed by the collective knowledge of members of this group.

Thanks again.

In the first one BALANCE is “what’s left” (perhaps in a financial sense) and D is daughter. Level headed is the definition.