Sash weights are going to hit one another--it isn't a problem. They are tube-shaped, and will not catch. Tie the cords to them with a sash knot.

Not sure why you had to cut access--all the windows in my house have access doors in the jambs held in by screws. If they aren't there for some reason, you can carefully pry off the vertical side trim to access the pocket.

There are these elongated modular sash weights that came to mind.
Casey

Here is a link that might be useful: modular sash weights Killian's Hdwre

You could also replace the weights with pullman spring balances and then insulate the weight pockets.

Thanks so much everyone, these are great suggestions! Columbusguy, yes most of the windows in our house have access doors too, but for some reason this tiny window did not. I chose to cut new ones rather than remove the trim thinking it would be easier...although I am not sure that was the case given the tiny plumes of smoke that resulted ;).

Once you learn how to remove trim without splitting or cracking it is is easy.

Nails are pulled out through the back to avoid damaging the show surface.

Start with an old 5 inch drywall knife driven into the joint of the trim to the wall at one end of the trim (for window casing the sill/stool is the best place to start after using a knife to score the paint joint of casing to stool) then a second one right on top of the first knife.

The use a cats paw between the knives to start leveraging the trim up.

When it has moved about 1/16 t 1/8 inch (depdns on legnth and strength of the casing) move up about 5 inckes.
You should be able to just remove the cats paw, and the knives.
Repeat driving and prying.

When you have enough clearance you can use a wonder bar with some backing (a pices of #10 steel plate about 12 x 12 works well to avoid damaging the wall) to pry the molding further.

Keep moving towards the other end prying a little at a time and them moving.

As the nails start to slip out it becomes easier and easier to pry.

Once the piece is off, clamp vice grips onto the protruding nails and pry them through the back of the trim (an wonder bar works well here).
Always pry towards the larger part of the piece, never towards a short end.

Be sure to mark the piece for location so you can put it back in the same spot.

I usually mark room, a window number, and then a side, and then another number or letter.

Put the same markings on the now exposed edge of the window casing.

You know, I have never understood why removing nails from the back is better? What I've usually done is to drive them back through so that the heads project from the face, and work them out--or, if I'm putting the trim back in the same place, leave them and use them in the same holes to reattach. :)

"why removing nails from the back is better?"

It avoids damaging the show face.

Depending on the size of the nail head (a 16d finish nail has a pretty large head), how well the countersinking filing was done, and what filler was used you can end up with rather large divots in the show face in a detailed molding pattern.

Now you have to repair all the damage and make sure it looks good.

If the wood is going to be (or is stained) the repairs become much more difficult.

I have pulled and removed very old molding and trim (even built up) and then put it back and no one can tell it was removed.

The hardest part was matching the filler for the new nails.

Pulling from the back produces damage on the hidden side, so there is no repair work.

Using old nails in the same holes is an invitation for loose trim.

This post was edited by brickeyee on Sun, Feb 3, 13 at 11:58

In case anyone ever has this problem in the future, we ended up buying 1lb lead square cod fishing sinkers and threading them on key rings to fit the sash rope. These weights were the perfect size for our small window and don't catch on each other like the old ring-shaped ones did. the window is now all closed up again and working great! Now that I finished up my "practice" window, time to unstick the two larger ones in our guest room, fix their sash cords and strip paint off of the window hardware around the house!