Help! High Throttle hesitation

Dreaming wrote: One more fun fact for Ken The secondary plate seems to have a 59 stamped on it.   the five is pretty lightly stamped, but I think that was the correct number.

Not a lot I can tell you about that plate except that it's the stock plate for a fair number of marine 4160's and info on it is not very easy to find.

I have one on a 4160 that feeds a 351 with gt-40 heads with no problem at all.

Probably looked just like this

Well? Any fun video to post?

Kevin

Kris, I am not a carb guy but your comment on Timing caught my attention.
You mentioned timing at idle. That is a good start but the important timing to measure is what you have at 2,500 rpm up to 4,000 rpm.   
Watch the timing mark move as you advance your rpm. It should advance smoothly as your rpm increases and max out around 35 degrees usually between 2,500 and 3,000 rpm.
The max or total timing number is the one that will give you performance or melt your engine.   If your distributor allows say 40 degrees at 3,000 rpm that is very dangerous for your pistons.   The only solution would be to recurve your distributor or back off the idle timing setting till your max is proper.
If your timing does not advance smoothly, if it jumps or does not move at all you need to go inside the distributor and repair it.
If your distributor as it is set now at 11 degrees is only at say 30 degrees at 3,000 you are leaving power on the table.   You can add idle timing to move your 3,000 rpm timing up or get the distributor re curved.   
Others that know the 351W better can give a better idea of the exact timing curve preferred but in general this is what you need to be aware of.
There are two ways to verify this. Any speed shop sells timing tape that you put on your harmonic balancer or you can measure exactly how far it is from 0 - 10 on your boat and add a new line at 20,25,30,35,
The easy way is to use a Set Back Timing light that allows you to dial in how much timing you want and use your normal timing marks. These are available for $80 or so and help.
I hope it purrs next time out.

Timing is rpm driven, it can be verified while running on the driveway in about 2 minutes. It sounds like you should be I I good shape but verify for peace of mind with your brand new engine.

So I am happy to report that it was a great trip to the lake this morning...   I was able to take 45 minutes on the ramp since I had the whole place to my self.   I checked ignition timing and found that it was accurate at 3000 RPM, ( 35°) and my 11° was good as an initial timing set point I think.   I also was able to work through the throttle/trans lever adjustment that I have been unhappy with.   Power was good with the replaced main breaker, so I launched the boat and spent about 2 hours of run time on the lake.    The throttle hesitation is definitely gone, and I varied the RPM from 1500 to ~4000 without spending too much time at any one RPM.    The carb rebuild was a good suggestion, and helped a lot Thanks to KENO and the others of you that chimed in.
    I liked the way the motor started better before the carb rebuild, now it takes a couple of throttle pumps at the ramp to get it to start cold, but I also noticed that the choke opens very quickly, so I may need to read up on delaying the opening a bit.   Over all, I am pretty happy.
I still have a little bit of a drive line vibration, but I suspect that is a prop issue.   I guess I will work through solving that as well, but it will likely take a back seat to the next few hours of boating time and getting the engine broken in.   

Well done, Kris!