I don't think ink because to make ink there's a metallic additive. Usually iron or copper. Both chemically 'stain', i.e. bind to the stone. This stone isn't marked in this way.
Most fishing net weights are relatively simple, with a groove of some kind that allows a rope to be knotted securely around it.
Like this.....
http://dirtyrockhounds.proboards.com/index.cgi?board=artifacts1&action=display&thread=3235
or with a hole that serves the same purpose, such as these ones.....
http://www.finds.org.uk/database/search/results/material/2/page/12
http://www.johnhextfremlin.com/A stone age find by JHF.htm
We do know of carefully grooved sinkers (I think the Americans call them plummets ? ) that are attached to lines for fishing too.
Short article here.....
http://www.jstor.org/pss/278523
and there are the beautifully worked sinkers (showing that they are not necessarily crude things) such as these from haematite.....
http://www.lithiccastinglab.com/gallery-pages/2007augustplummetspage2.htm
generally safe to claim that all 'plummets' are teardrop shaped though.
A lamp is basically a reservoir with an orifice that supports a wick. I don't think that's likely simply because of the size of the piece. Four or five wicks would need a lot of refilling.
The fact that the holes connect suggests somekind of threading, but the stone shows no wear patterns from ropes rubbing. If it were for threading, then I would think 'tied' more like a button....but why go to all the effort to keep the base in one piece ?
We split materials like willow and sinew, but why the ornate grooving ? and those are generally more like a simplified lemon squeezer; they're called brakes if anyone's looking for them
There are small dishes with loops on the inside base that are intended to wet flax fibres of a roving before they are spun. I don't know what fibres were used in the area this artifact was found.....but why five holes ?
I suppose it 'could' be a cordage winder. Thread four lines in and spin while pulling one out ? We'd use a 'crown' for that though and again it's more like a simplified grooved lemon squeezer, sort of, think sized up.
Basically, I don't know.
I suspect it's too big to be a personal adornment. I think it's too small for a multiwicked lamp. I don't think it's ink because there's no chemical staining. That it was found in water generally would indicate that it was somehow connected to fishing or..... you guessed it

Ritual depostion
Someone must know, surely ?,
atb
M