Evening supply - when does it catch up?

[MuddlingThru]

DD is now 16 weeks and most evenings still feeds to sleep as tiredness takes over before she has had her fill. She often settles herself for naps. Also if I have left her in the afternoon with my mum with a bottle of EBM and my supply therefore has a headstart she manages to take her fill and go down awake at bedtime and settle herself. So I am not particularly worried about it. However it does make for a disturbed or short evening as she either wakes 1/2 hr later to finish her feed or only makes it to about 9.30pm before needing the next feed. I initially assumed that as bf supply increases to meet demand that as the weeks went by my supply would increase and dd would also stay awake longer and would therefore be able to take a full feed but so far this doesn't appear to be the case.
I have tried starting her feed earlier so that she has more time to feed before tiredness takes over but then I end up feeding so early that she wakes by 9.30pm.
I was therefore wondering what other people's experiences were. Does it improve when they start weaning and milk becomes a less important part of the their diet? Is there anything I can do to help the process along so that I can have more of an evening to myself? At what age realistically can I expect her to easily finish a feed without passing out through tiredness?

[MuddlingThru]

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