If you look at the link of the pocketwatch database for the serial number and you go to the parts list you can go to Springs and I snipped out an image. So we have an Elgin part number and a strength as an added bonus you click on the part number and you get this link
Fortunately it looks like that particular hairspring goes in a lot of different watches. That's the good news the bad news is we still have to find one and you're going to have to play with the screws to bring it in to time. When I get a chance I'll go look at my Elgin parts catalog and see what it says about the hairspring if there's any other additional information.
Then that is assuming that it just needs a hairspring and that it doesn't have a broken balance staff more than likely it's going to need a main spraying and if you're lucky that's all that's going to be wrong with. I don't like when parts are missing like any parts it suggests other things could be missing were not even right. As one of the cautions of buying off of eBay it might look nice and pretty in the picture but in real life that doesn't always agree with the pictures. On the other hand the watch that I bought that wasn't quite what should be scrapped for parts because I really needed one of the parts off the watch so it worked out at the end.