I'm replacing the brakes on my old Gitane which has Weinmann levers from the 80s(brakes were Weinmann 405s). I found a decent deal for Shimano Ultegra 6600 calipers. Would these be compatible? It seems like the cable pull changed for the Shimanos with the 6700 and the 6800s as well, but I can't find information about the older calipers with old levers.

For what it's worth--I have an '84 Peugeot that came with those crappy Winemann brakes. I put Shimano Ultegra dual-pivot side pulls on both the front and rear. I'm using the original Winemann brake levers with no problems at all. It's a classic case of simple is better.
Jon

Its all in cable pull ratio, mechanical advantage , or the various parts..

old cable out the top levers have a measurable cable pull somewhat greater
than cable under the bar tape brake levers , but less than
a hand lever made for V/ linear pull long arm calipers..

I have no way of knowing if 'Ultegra 6600 calipers' will even reach your rims..


..

Both my bike and the Ultegras are short reach (39-49). Are the 6600s made for over the top or under the bar tape?

6600 levers have under the tape brake cables and side exit (not under the tape) shifter cables. As for the calipers cable routing makes no difference.

Read it as keeping the brake levers, on the bars.. but changing the rim brake caliper, myself..

Not sure if anyone clearly answered your question, but the correct answer is: Yes, 6600 calipers (designed for super SLR levers) will work fine with your older levers. 6800 calipers would not, nor will any caliper that is considered SLR-EV. 6700 calipers are 'new Super SLR' and seem to be somewhere in the middle. Shimano claims that 'new Super SLR' levers will work with SLR-EV calipers and vice versa. They also say that new super SLR levers will work with super SLR calipers (but not vice versa) though with slightly less braking power. I would not bother trying to use those calipers with older levers when 6600 are readily available and have a more classic look.

Go digging here if you want to see all the compatibility options for yourself: 2018-2019 SHIMANO Product Information Web