I have just bought (very cheap) a Weatherby Synthetic (in a wood stock) second hand in 243. It seems to have a 24" Barrel #1 and a very lightweight action. I'm not sure if this is a standard action or a lightweight one.
Anyway, it shoots terribly, it runs about 2.5" at 100 yards using homeloads (42 Varget Nosler 70 BP)
and 3" using factory 55s (Winchester Supreme)or Federal 70 BP.
I want to keep the rifle, but need to know what the best progressive upgrade will be?
I have looked at a McMillan and HS stock (would have preffered to keep the wood). My only concern is that if I pillar/glass bed the action, if I need to add a new barrel I will not get away with a heavier profile as the woodwork is very slight.
I had a similar issue with a 22-250 Weatherby (1968) and got it recrowned and it all fell into place.
Any ideas??

With such a light setup, it could be an issue of harmonics in the barrel. May I suggest a cheap first step, try a Limbsaver Barrel Deresonator.

http://www.cliffsgunsmithing.com/Catalog_Limb_Saver_RE.htm

-Spencer

First things I look at when a customer comes into the shop with your story is; A) guard screws for tightness and to see if there is any binding of the action when tightened; B) bore; C) crown; D) forend contact with the barrel; E) scope and mounts; F) trigger.

If the bore looks good, almost every factory gun that comes into the shop gets a new crown. You will never know how well that gun will shoot if the release of the bullet is in any way flawed.

As far as those Limb Saver Deresonators go, make sure that the barrel is free floating before you slip one on. If that device is going to do anything other than sit there and look ugly, the barrel has to be free of any other contact.

have you tried free floating the stock

IMO the first step in accurizing is glass bedding and free floating the barrel.....

After that one can handload for results...

This assumes things like scope and mounts are properly done.

Just out of curiosity and as a word of advice to others, are you using any kind of rest like a Lead Sled? My friend bought a new Kimber Montana in 7mm08 and got so mad with it that he called Kimber to make plans to return it. It would only shoot about a 5 inch group at 100 yds. I had him check the action screws, scope and mounts, etc., all of the good advice you have gotten so far. I he eventually mentioned he was shooting it from a gun vise and I suggested he try the usual sandbags. He said no I'm sending this piece of $£1! back!!! That afternoon he called me from the range and left me a message, "It was the gun vise". I was shooting factory loads into 3/4 of and inch. I had the same experience with my 458 and my Lead Sled and eventually got the groups I was looking for off of sandbags. Just a heads up. If you are not using a lead sled or vise, go thru the action screws, scope mounts, bedding and then as you mentioned the crown. Good luck.
Doug