You could refer to Canada's Safety Code 6. There are equivalent standards, but that one's a good start.

"tired eyes" isn't the usual symptom of RF hazard.

 

I have a daughter who does glassblowing professionally.  The ovens/glory holes give off a lot of IR and ultraviolet light.  The concern is if the shielding eyeglasses are reducing the optical radiation enough.  On a recent eye exam, here opthomologist told her "If your eyes are getting damaged, you will feel something going on".

So, if you are feeling like tired/dry eyes, I would not rule it out.  Microwave radiation will primarily heat up the eye, so you might be feeling some of that.  Most radars are set up with antenna gain to beam the energy far away from the ship, and not into the bridge area, so it is not very likely you are getting doused with microwaves.  Never the less, it is easily testing with the right microwave field probe.   

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What kind of ship? military? Describe the antenna hardware and the ship a bit more.

Normal Marine radar does use alot of peak power (2 kw) and not much for average power.

It's unlikely that it's RF radiation unless you were working in a location that not many people access and it's right near the antenna. Eyes are sensitive because they don't have much blood circulation to remove the heat.

 

Higgler, its a merchant tanker using commercial navigational radar like; Atlas, Sperry Marine.

"..the more, the merrier" Genghis Khan

 

Here is a high power Sperry Radar, looks like for larger ships, http://www.sperrymarine.northropgrumman.com/Products/radars/anapn242/specifications  

Average power calculated for this Sperry Radar varies from 5 to 20 watts, depending on the mode they use (long range vs. short range) peak power is 25000 watts per their specs.

That's a level you won't want to work at for a long time. Especially if you're right at the dish. In the cabin, on the deck, absolutely no worries at all. You have to be right at the antenna.
It's very unlikely to hurt you unless you were working  less than 10 feet away, same height, and were working for many hours or even days.  

At around 8 to 12 feet away from the antenna at the exact same height, you'd get the peak power density (0.4 D^2/Lambda). I've been next to a dish antenna with 4 times that peak power (100,000 watts), and only 15 feet away and didn't even know it was on.

If you were next to another transmitter, you'd have to provide the model and distance from it for an assessment. I'd rule out the radar and lean towards other sources if there was a true radiation hazard. You'd need other people to probably have similar discomfort too if you want anyone to believe it. The biggest effect I've heard of in the old days, from a 15 year period at 1940 to 1955, there were 23 kids born to the Engineers of the Raytheon Waltham Massachusetts Radar Lab, all girls.

good luck,
kch

  

Navigational radar uses a highly directional beam that will not affect anyone on deck. Power densities are negligible.

For a comparison point, consider the low-frequency non-directional beacons that the Air Force used to have in the Portuguese Azores. (Current versions are different) Transmit powers were such that enlisted men drew arcs off the arrays with wooden handled shovels or stood near them to warm up on a cold day. My father was one of those guys. He later had two kids and is now in his 70s.

Short version - I wouldn't worry about the radar. You're more at risk from ultraviolet radiation and reflected sunlight from the water surface. Those radiation sources can and will damage the eyes.

 

Were the two kids both girls? Raytheon Radar Engineers history says Microwaves may make girls.
Raytheon Waltham Mass. 23 kids, 15 years, all girls between 1940 and 1955.
 

After a quick check of my pants, I'd have to say no.

1 boy, 1 girl. For what it's worth, he didn't have kids until about ten years later.