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Have you tried lubricating them. If that didnt work than the springs on the handles maybe shot. Vendors carry a small spring clip to act as an assist or you can replace the handles.
FWIW - pulling those handles is one of the toughest jobs there is on a Corvette. I never pay to have work done on a hobby car - yet I paid to have that done by a mechanic... wasn't cheap, but since I still have my sanity; I figure that's worth something (shush peanut gallery )
In most cases when the handle sags it is from the pot metal housing and lid wearing out on the steel pivot hinge pin. The hinge pin is steel and hard, the housing is made from what we call pot metal and soft. The best way to tell is to look and see if the lid is actually dragging inside the housing cup.
You can try lubrication in the hinge and you could install “Helper” springs. Sometimes the helper springs work but in most cases it is only a band aide.
Take the plastic splash sheild out of the door, and take the 3 screws out that hold the latch in place, allowing it to drop down, and replaceing the handles becomes a lot easier. I' ve done a lot of projects on mine that I would consider harder than door handle replacement. FWIW, I'd just go ahead an replace both of them with USA made only, as the quality of offshore replacements is suspect.
Not to hijack, but since we're on the subject of door handles...On my recently-acquired 81, the door handles both work, but seem VERY stiff at the point where it starts to actually open the door. The springs seem to work fine, in that the handles return to surface level once the door is open, and you don't have to push hard until you get to where it starts to unlatch the door, but at that point, I have to almost use two hands to push down hard enough to release the door. I'm assuming it should take that much effort to open the door...any thoughts? Opening from the inside latch doesn't take much effort at all.
DO not insert that "spring" upside down...I did that on one of my 76's door 3 weeks ago...and I still have not taken the door apart and attempt to remove the spring..
I just ordered a new complete door handle..
I've replaced the door handles on all 3 of my C3's and I honestly do not understand what is so hard about doing it...not time consuming and definitely not hard to do...