Weather radio freq is in the 162.xxx mhz range and CH 16 is 156.8 mhz
Not exactly "close" but certainly same "band". If you have multiple antennas in close proximity ( ie: same roof ) it is easy to overload a same band receiver IF ( one of several things ). Possible problems include poor connections, failed filter cavity, out-of-channel operation, "dirty" operation ( harmonics ) etc.
Someone needs to inspect both xmit and rec systems, using decent equipment ( as well as a good eye ). The "quick fix" is separate the antennas. In this case there are likely two ( competing ) govt operators both of whom think the other guy needs to move. Of course, actually maintaining both systems properly ( FCC requirement for ALL operators, incl govt ) would result in peace all around.
In the absence of test instrument data, NOAA should find a different roof...
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btw: In the case of an amateur operator, even if the neighbor who is getting interference has an "incompetent" receiver ( fails to "accept interference" ), it is almost always the duty of the operator transmitting who will need to resolve the issue.
In this case, it is NOAA transmitting, therefore, it would normally be NOAA who gets to do the sleuth work. Or, they could simply remove the interference, ie: move the transmitter.