Why is signal from AirPort Extreme weaker in some rooms?

The "why" could be for a number of reasons:

1. Wi-Fi interference
2. Wi-Fi signal propagation physics (antenna design, fade margin, noise floor, range, etc.)
3. The client's wireless capability.
4. An aging AirPort Extreme base station.

The most likely reasons, in your case, I suspect would be items 1, 2, & 4 above. LaPastenague has already covered some potential solutions to remedy this.

The best way is wire your house with ethernet.. Add Access Points (AP or WAP) as required. You can use another Airport as AP but there are better products now.

The second best way is to buy new wireless mesh which is what Apple now sell. (Linksys Velop, Netgear Orbi, Eero)

The worst way is to buy another Airport Extreme and use Extend wireless. Apple ceased production of routers in 2018 so it will need to be second hand.

I assuming that you are referring to is your WiFi speed? If so there are a lot of things that can affect it:

1. Distance from the router
2. Obstructions (walls, brick, metal, etc.)
3. Number of other networks which are using the same channel. Control click on WiFi icon/Open Wireless diagnostics. Try to find a channel with is not being used. Channel selection is a major topic in itself. 1, 6, and 11 are often good if few conflicts. I my case there are 50 local networks fighting for a limited number of channels.
4. What WiFi protocol is being used - AG, AN, AC, AX. Some network signals travel farther; some are better at obstructions.
5. Do you have a 2.5 or 5 Ghz network?