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it looks like your arrows are pointing towards the vacuum secondary's but it can't be leaking from there... i would guess it's the float bowl behind it? idk... either way you can buy a kit to rebuild it for like $40-$50 or you can get a new holley 600 street warrior (that's what it looks like you might have?) or brawler for around $400
looks potentially too far to the center to be the float bowl gasket, but it could be the needle not seating and over filling the float bowl (somewhat common with ethanol fuel in carbs) or your float could be adjusted too high/or you're on a hill or the float itself could have a pin hole in it and it's no longer functioning? those are all guesses
might be able to run a bunch of berryman's or some other carb cleaner directly filled from the vent tube and see if it cleans out the needle and the seat (if it's that) but it would likely be better to take it apart and clean and re-gasket everything because you'll be able really clean everything out and if it's not the needle/ seat or the float, you'll catch it with the rebuild.
this is not necessary,,, you can do the whole thing with berryman's when you take it apart, but if you bought an ultrasonic cleaner for like $40-$50 you can just take it apart and drop the parts in there, go to sleep for the evening, wake up and put it all back together.
i don't know for sure what you have but it looks like a holley street warrior, but it looks like it and it's a common parts store option to replace the OEM carbs.
what engine do you have? a good target is to double your displacement in inches with cfms. like a stock 302 would run pretty good with a 600 cfm carb. i have a 650 on my 390 that the previous owner put on and it runs fine, but i'm likely missing out on potential power in the higher RPMs (which i don't care about). I do think the brawler is a little nicer of an option and a little cheaper. you also obviously have vacuum secondary's and an electric choke. a new carb is going to, at least require adjusting the idle and idle mixture screws. some guys can do it by ear, i can't and a vacuum gauge is like $20
I'm reversing my opinion on it being a stuck needle or float issue... idk what i was thinking, if that was the issue it would leak down into the engine and no out of the side of the bottom.
ahhh the street warrior series comes as big as an 850 which would be undersized, but again, you likely won't lose anything under 5k rpm... i see a lot of guys run 750's on their 460's. i'm sure its fine in normal driving conditions but i'd personally aim higher.
the brawler is basically a double pumper design and comes in a 950 and a 1050, but above 850 they are really race style carbs so you can't get vacuum secondarys or electric chokes (i actually don't think they have chokes at all) with the double pumper design it will likely feel like you have better throttle response since you have accelerator pumps on both the primaries and secondaries