RR,
  This thing of wgt. for an offhand rifle is a very subjective thing and you're gonna get a lot of answers on what others feel is right.

  First, you'll have to decide what you can handle right now, or with a little practice.

  Second is how much practice do you want to put in to be able to handle a heavier rifle.

  The stronger you are now the heavier the rifle you can handle to start with.

  Some of the old Schuetzen shooters could handle rifles up to 16 pds. or so. This was an extreme tho and rifles weighing in the 10 to 12 pd. range were mostly what was used. For offhand shooting my BRC Ballard .22 with scope weighs just under 12 pds. and Schoyen/Ballard with scope about 11 1/2 pds. Rifles in this wgt. range seem to handle the best. But unless you're in fairly good shape it's gonna take a few weeks of constant practice to toughen up to them.

  Caliber is another thing to look at. I won't try and talk you out of the .38/55 as it's a good caliber, but for offhand work I think you'd be better served with a .32/40. If you get into this sport you'll probably want to try a 100 shot match some day. Also, what with re-entries in most matches it's easy to shoot 100 rounds in a day. The wgt. of the rifle and recoil of the .38 will really wear you down before the end of the match.

PETE

An observation.  In the last three years I have seen one Sharps type rifle at EG and probably a dozen CPA's.

On Weight.

I have 2 CPA's and 3 28 inch # 4 Barrels. 38/55 32/40 .22 LR All of the Rifles with either a Unertl or Lyman STS scope weigh about 14 lbs.  Almost 2 lbs are the scopes. The 38/55 is BPC stocked and with Iron sights makes weight for BPCS so it's about 12 lbs.   

CPA will and does often set rifles up with # 3 barrels and you save some weight. One of my repro Stevens Catalogs says the following 

28 inch # 5  = 9# 10 oz
          # 4 = 7#  5 oz
          # 3 = 6#
          # 2 = 4# 15 oz

As far as how they look, I have seen one # 5 and it's real big, Usefull only for bench rest. 4's look right and so do 3's. I think a lot of old Schuetzen matches were shot with # 3 Barrels.  A 2 looks like a sporter. I also have a # 2 barrel in .219 zipper and it's a good field sporter rifle. Not a target gun.

The  Schuetzen stocked Rifle does not feel as heavy as  the BPCS stocked rifle. It balances better offhand and the hook buttplate and palm rest help hold the weight. For an offhand rifle it's just right.  I shoot the Hudson Match and shot 100 shots offhand in one day with the Rimfire barrel last Friday. By the last few relays I do know it's heavy but would not want to trade it off for a lighter rifle score wise. With the CF barrel I have shot the Hudson in one day but usualy go for two days to shoot the string and weight is never a problem.

I shoot light rifles too ,offhand, modern Silouette both HP and Smallbore. My HP outfiit weighs 9 lbs and smallbore 7 1/2 lbs. 
They are fine in those weights and thats all the rules allow.  But weight is a real advantage to scores. If I could shoot the Scuetzen CPA in Modern Smallbore Silouette matches I bet I would shoot a lot higher score. Of course so would eveyone else if Hooks palm rest and unlimited weight was allowed.

As far as CPA's service. I cannot say enough good things about them. They are real good in turnaround, fair dealing, you name it.  I have owned the one Rifle about 15 years and the other 5. Have had extra barrels alterations and re-stocking done over the years. Never needed a repair but expect if I did the same good service would be evident.  I wish all gunsmith and custom builders worked as well as CPA.

Boats

Ranger Rick
I have two CPA's and can't say enough for their great service and great accuracy.
Bob

Ranger Rick

I should clarify,  The weights I gave were for Barrels only.  Add 4-5 lbs for the action and buttstock. Depending on the wood and buttplate. And old style scopes weigh almost 2 lbs while modern scopes weigh about 1 lb.

If you live close to CPA they have lots of rifles and stocks in all sorts of configuarations you can try.

Boats

Ranger_Rick;
You will be MUCH happier with the CPA for Schuetzen. Get a Schuetzen stock ( I have a CPA with Pope stock - I would not get so radical design next time but would prefer the Stevens Model 52 {pistol grip}.

If you have a problem with the weight, get a #3 barrel. If not, get a #4. I have a #4 and getting older, wish it were a #3.

At any rate, the CPA, with the Model 52 stock and hooked buttplate and palm rest is competitive at the highest level right out of the box (keeping in mind that it takes a shooter and a competent bullet caster for these rifles to reach their potential. It also requires a really good scope and/or excellent iron sights with any rifle to compete. I prefer a modern scope (they have excellent optics and are lighter) but many prefer the traditional Lyman Super Targetspot or Unertl. Scope powers up to 36X are commonly used. I happen to use a Weaver T36.

Dale53

Ranger Rick

Dale 53 is right about the stocks. My Schuetzen is the high comb Pope model and I like it a lot.  But I don't recomend it for everyone. I have spent some time in Free Rifles and Air rifles so the high head positon is not so strange to me. It's also a 32/40 switch barrel to .22 lr which is a good competitive outfit if you want to stay traditonal looking. You can shoot all the offhand matches and none of the bench matches with a rig like mine.

My older CPA is BPCS stocked and I am going to change it to a Stevens 52 stock. The plan is to use it with Black powder, it's a 38/55 which is about perfect for Black and is a proven performer as it is. It does recoil more than the 32/40 200 gr and I also plan to change the  bullet from a 300 gr spritzer to something lighter for Breech seating,  The Stevens 52 stock can shoot bench although not the best solution.

The question of Bench/Offhand is pretty difficult unless you shoot two different rifles. I stay offhand so don't have to make any concessions stock wise.

You may want to get one of the reproduction Stevens Catalogs to look at. CPA will build to any of the old model numbers.  I would bet CPA has built more high grade and target rifles than Stevens ever did.

Dale is also right about the Speed lock hammer. I switched both of mine. (Paul Shuttleworth turned them around the same day) They do like softer primers however and also switched to 2 1/2 rem pistol primers with very good results.

Boats