What do you mean by “the part he put to seal the door”?
The only way to make this lighter is to remove material, or add a lift assist mechanism.
A simple counterweight system might be quicker/easier than rebuilding the door to be lighter. Simplest way I’d attempt this, is by adding eye bolts to the top edge of the door and the nest box, then add a string and counterweights. A spring and chain could also work, but spring loaded things might not be a great fit.
To reduce weight of the door I would likely reframe the back side of the slat siding. Such as swap the 2x4 lumber with smaller dimension lumber (like using only 1x2 lumber) or lighter-weight pieces instead of what looks like heavier reclaimed old-growth wood.
Might even be able to remove most of the 2x4 frame and go minimal - like just fix the two slats together with 3 vertical braces, and either hinge directly off the siding or on the braces where it’ll be strongest. Minimizing the internal frame will also give you more accessibility
An observation of having a heavy flip-down nest door myself - the design of having a horizontal brace inside the door frame along the bottom, adds a potential issue of nest bedding getting sandwiched between the door frame and nest box frame, when you open/close the door. I left a finger thick gap in that location to accommodate buildups of bedding, I do have to clear it out every now and then to close the door smoothly