I'm looknig for some advice. A member of my family died recently and I'm tasked with selling their record collection.

There is a copy of 4 Track Demos and I'm struggling to work out whether it's the original or the 2009 re-issue, is there anything that distinguishes the original from the re-issue?

I thought it was the original as:

She has a numbered version of Dry so clearly bought early releases
The vinyl seem too thin to be 180g, which I believe the re-issue was pressed in
however, there is no sticker or any evidence that there was once a sticker on the front cover.

Can someone help me identify which version I have?

Have you checked Discogs.com? There's a huge catalogue of details about different versions of possibly any record ever produced.
Try checking the catalogue number of your copy:

https://www.discogs.com/it/P-J-Harvey-4 ... ster/52570

Thanks, I tried there first and that's where the confusion started as the details on Discogs would suggest it's the initial release except for the lack of sticker, which suggests re-release.