Instead of just disposing of weak alkaline batteries, is it possible to extract the remaining charge to charge re-chargeable batteries? I imagine theoretically you can attach the weak batteries to a battery charger, but how do you ensure that the charge is in one direction? Or is it just not efficient to try to extract the remaining charge from the weak battery before disposing of it?
You need a device commonly called a "joule thief" -- this is a DC to DC voltage converter that can take a low voltage input (like what you're getting from a nearly discharged primary battery) and output a higher voltage (like what's needed to power a charger circuit and store energy into a rechargeable battery of some kind).
These are fairly simple circuits, and variants of them have been used to charge capacitors in electronic flash units to around 400 V with input as low as 1.5 V for decades.
However, be prepared to be disappointed with how much actual energy you can extract from a battery that's gone flat enough to drop below about 1.2 V per cell. That low voltage combined with the low current capability of a battery or cell that's nearly used up means there isn't much to get -- you're basically in the position of trying to fill your car's fuel tank with the little splashes of fuel left in dozens of "empty" Jerry cans -- it might be possible but it's a desperation move, something you'd only attempt in a near-emergency situation.
This would be like trying to fill a water cistern by gravity from one that is lower to one that is higher – impossible. It seems to be an XY problem. If the actual problem is not to waste the remaining energy in a battery, here is my hack:
Some of my battery powered appliances that are running all the time need very little power and a new battery lasts for several years. Some examples are a kitchen wall clock, and a min-max thermometer.
Others are more power hungry/thirsty, and don't even run all the time, such as a cordless phone, and a flashlight.
When the battery in a hungry device weakens, I keep it to use in a low power device.
By doing this I have extended the use and life of the battery.