That last poster is correct. To add to the convo: The weight of water displaced is equal to the weight of the floating boat added, so the net weight on that "bridge" is the same.

In a small scale closed system, if you placed a boat in a bowl of water (and the water did not overflow) and measured the weight on a scale, it would increase equal to the mass of boat.

If you imagined a FULL bowl of water (nearly overflowing), then added the boat... all the displaced water would overflow out of the bowl and away from the scale. If you re read the scale after the boat was added; it would show nearly the same as weight as the initial weight of the bowl and full water. (The differences would be things like surface tension, or too much water flowing out; but it's like the bridge scenario.)

Now a really good follow up question for you (don't google it first):

A) Imagine the same closed system (with a bowl that can't overflow when you put something in it) on a measuring scale but instead of putting something that floats, it's something solid like a steel ball...

-Water + bowl = 100 grams -Steel ball = 50 grams.

What would the scale read when ball is added and inevitably sinks to bottom?

B) same scenario as A except you lower the steel ball half ONLY way into the bowl with a fishing rod and string. imagine the ball is being suspended and prevented from sinking by some massless string. I put a mass gauge to measure the tension on the string and it equals 50 grams, the mass of the ball.

So the masses are the same above in Scenario A, what does the measuring scale read when the steel ball is only halfway in the bowl and being held up by tension from the string?

P.s. I'll probably have to edit this post cause of sentence errors as I'm typing from my phone.