"the tailpipe opening is beneath the trunk instead of sticking out from behind the rear bumper."
I've always found my Volvos to be sensitive to where the exhaust exits with made up systems. In the wrong spot and those smelly fumes get sucked right in. Changing that may take some awareness of your exhaust away--at least while driving.
With a carb you're not going to be able to match a fuel injected car running through a cat but it's likely your mixture needs some tweeking. Another poster suggested checking the jetting of what you have and I'll 2nd that suggestion. It's not hard to do--really all you need is a screwdriver, needle nose pliers and maybe a metal paper clip--and paper and pencil for recording the findings.
The first owner of the Weber may have tried to do some "jetting" (and who knows what was there to begin with). The first inclination is to mess with the main jets in the float chamber. Go bigger and the car feels stronger--so going a little bigger yet is the path most would take. What you want to do is record the main jets, the air correction jets and the idle jets. The paper clip is for fishing out the emulsion tubes--although those are something only an experienced (or adventuresome) owner would likely touch.
Report your findings--maybe it will be as simple as finding "way to large" main jets---the correct jets are usually in a fairly narrow band.
I have a good selection of used jets I would be willing to "loan".
It would be best to have a "top" gasket on hand but the tops usually come off with the gasket intact. Loosen all the screws to the top cover and tap the cover with a screwdriver handle to shake it loose. Remove the clip for the choke rod to high idle cam and the top should lift straight off.
When "jetting" a carb you should move from rich to lean. When a too lean condition is reached you'll feel it in the driving--at that point go back one step to richer. -- Dave