There has to be. Adding 3 pounds is only a 1-2% increase to gravitational drag.

Another thing that can have a big effect on climbing, albeit very circumstantially, is gearing bottom-out.
My 1983 Miyata 710 weighs about 5 pounds more than my Emonda, and on medium-grade climbs it averages a couple percent slower. But the old bike has a 41" granny gear (42-28 on 27 x 1 1/8 tires), while the Emonda has a 32" granny gear (34-28 on 700x25), and sustained steep gradients can be a serious problem for me on the Miyata. There's one climb in my area that where I've put in hard efforts on both bikes, and my PR on the Emonda is about fifteen percent faster than on the Miyata.

How do the front-end geometries of your bikes compare? A bike with less-floppy geometry can take less effort to stabilize at low speeds when you're rocking it back and forth out of the saddle. It's hard to quantify the exact impacts of this, but it can definitely be felt.

Is it possible that your climbing pedaling form just doesn't agree with the flex behavior of the slower bike? A lot of bikes seem to be pretty agnostic to pedaling form, but some are less so. The 1979 Fuji America that my grandfather gave me has a ridiculous amount of attitude... it can feel absolutely lovely to pedal, but it feels like it's kicking back and fighting with my legs if I don't get into certain rhythms with it.