Could airline tires be deflated in mid-flight to reduce weight?
You want to reduce weight by removing a few kilos of air, and adding an equal, if not greater, amount of kilos of pumps needed to reflate the tires (see David Richerby's answer for details), not to speak the additional costs incurred for periodically checking the correct functionality of said pumps, that would be marked a &quot;safety critical&quot; (because a landing with deflated tires would have really bad consequences) and require being checked quite often.
So, feasible maybe. Safe not really. Meaningful I don't see how, particularly when there is the risk of tire burst, as shown in this video linked by March Ho.
A lighter alternative would be to use bleed air from the high pressure section of the engine, but it would still probably(*) be heavier than the air you are pushing out (you need heavy duty pipes to transport high pressure air from the engines to the wheels), and not a good solution safety-wise: what would happen if you have to land without engine power?
(*): as user3528438 mentions in their comment, it would depend on the wheel size.
Additionally, this Goodyear manual provides insight in some other problems: (emphasis mine)


ALLOW 12-HOUR STRETCH AFTER MOUNTING

All tires, particularly bias tires, will stretch (or grow) after initial mounting.
This increased volume of the tire results in a pressure drop.
Consequently , tires should not be placed in service until they have been inflated a minimum of 12 hours, pressure rechecked, and tires re-inflated if necessary.

It means that the tire needs adjusting after being inflated, possibly removing the possibility of inflating and deflating it continuously (or, alternatively, you have to reinflate it at least 12 hours before landing). Note that this manual is written for current operations, that call for a replacement/inspection of the tire if pressure drops below 80% of nominal value. Procedures should be rewritten for inflation/deflation cycles, and this could be a factor.