If you're not sure whether the signal that you're picking up is from your neighbour's router, then you need to change your router's SSID to something unique. If you read my Securing Wireless Networks page, then you'll see that changing the SSID is only one of the things that you can do to secure your network.

As far as weak signal and interference is concerned, there are several things to consider. If it's a weak signal then you need a wireless extender (I don't know anything about these, I just know that they exist).

If your problem is interference, then this can be caused by microwave ovens, hair dryers, or other wireless networks. It's a fair bet that your interference is caused by your neighbour's network. An easy way to remove interference from another wireless network is to move your network to a different channel (both networks are probably on channel 11 at the moment, so try moving yours to channel 1).

Also, if you're running WinXP, then you'll probably want to disable Wireless Zero Configuration.

My website