15 month old sleeping all night finally but nursing more in the day

Bethany, who spent the first 15 months of her life waking every hour or two
all night, slept through the night two Saturday nights ago and has been ever
since. She has changed her bed and naptimes, they are an hour or two later
(it's different each day) but she sleeps a whole 10 hours at night (isn't it
wonderful CY!! my mother said Bethany could tell I was getting fed up with
her and she decided she'd better start sleeping) and a 2.5-3 hour nap every
day.
Since she started sleeping all night, she is wanting to nurse much more than
before. Everytime I sit she wants it, everytime I stand still holding her,
she wants it. And one won't do it, she switches back and forth, back and
forth, for minutes at a time. About once or twice a day she'll stop and say
"Gone, gone". I wake up in the morning with very full breasts and I leak on
the side she doesn't nurse on first, so I don't think I'm drying up? I want
to start weaning her, keeping the bedtime nursing and the naptime one, and
the waking up ones(those are my favorite, when she wakes up and nurses), but
it seems impossible to do. If I don't let her nurse she has a full-out
tantrum, poor pitiful thing.
Marie