Hi,
Your Weber installation looks good!
What size chokes (main venturi) are you using in those carbs? What other modifications have been done to the engine?
That stumble might be incorrect idle jetting (which actually isn't an idle jet at all, but an "off idle" jet that functions when the butterfly first opens). It's probably either too lean or isn't enriching quickly enough. But, it could also be related to the accelerator pump, it's jetting, an even the secondary venturi.
By far the best thing you could do would be get some time on a dyno at a Weber tuning specialist to set up those carbs *exactly* for your engine. An experienced Weber tuner will have a selection of jets to swap out, while the car is on the dyno. Trying to do this "shade tree" style ourselves usually ends up costing a *whole lot more*, since we need to acquire many different parts and jets (4 of each, in most cases) to swap out on a trial and error basis. Any future engine/exhaust modifications will usually require a check and more minor changes to the Weber setup.
Due to the fender clearance in TR3, especially at the front-most air horn, you might consider having an air box made up. Might be able to get one done locally at a body shop or other type of sheet metal shop, or maybe even a local community college, tech school or high school that offers sheet metal and welding classes. (Or take a class and make one yourself.)
I don't think a low-profile air box will work with those longer air horns on the carbs (and I'd try to keep them as long as possible on a street car... short ones and full radius type are for high rpm race track work).
In case you haven't seen a Weber air box, take a look at
www.revingtontr.com The airbox simply mounts behind the air horns, which are then reinstalled and the air box cover put on. An airbox should have 1" clearance min., from the mouth of the carb's air horn, a little more if possible. Besides that, there an air box is little more than an box that can be opened on one side, provides a fitting for the flex hose and/or filter, fits under your car's hood and won't interfere with anything when the engine moves around normally.
I would recommend *not* routing the 3" air intake flex pipe out through the radiator shroud. Webers like to run in still air and you will get some ram effect at speed if you put the hose through the shroud (plus steal some air from the radiator, which needs all it can get in most TRs).
Instead, just put a filter on the end of the hose and clamp it to the fender or something up near the front of the engine compartment, where air can be drawn in as needed, not forced in. Perhaps near the RH headlight bucket.
Alternative to an air box are sock-type filters that just slip over and clamp onto the air horns on Webers. This type can mess with the air flow into the carbs, but that may not be significant, depending upon how highly tuned your engine is, overall. The wire mesh you have in place now could possibly be left as is to support the sock-type filter. If you want to drive the car until you get an air box made up, this might be a relatively inexpensive solution.
A third possibility, depending upon clearance, is a deep set of K&N oval filters. They make 3.5" deep version for Weber 40/42/45/48 DCOE, that fits over air horns up to about 40mm long (yours look like they might be a little longer). However, on TR3 the inner fender much be modified to make room for this type filter. Also check carefully for hood and other body clearance. It differs depending upon which manifold is used. (You can see a set of these K&N filters installed on my TR4's DCOE, at the link below by my signature, if you wish.)
One other thing, I can't tell from the picture, is there a support bracket for the Webers? The reason I ask is it's recommended in Weber installation manuals to fabricate some sort of support (this can be incorporated in the air box design). Now, I ran Webers on my TR4 for many years without any proper support bracket and never had a problem. It's got one now, though, because I've seen any number of Weber DCOE with one or more of the mounting ears broken off and welded back on. There's a lot of weight hanging out there on those four mounting ears per carb. Adding an air box will add even more weight, with even more leverage on the mounting ears.
Hope this helps.
P.S. You might take a look also at TerriAnn Wakeman's website for tons of info on Webers installed on TRs.
https://www.tjwakeman.net/TR/index.html is the URL.
Cheers!