Rejected transactions are disappointing, but it's better than the alternative: having your transactions in limbo for weeks, or thinking that your transaction was accepted when it was not. A "the transaction was rejected because it is too large (in bytes)." error usually happens when are probably trying to spend coins from a mining wallet or a coin faucet.
Bitcoin transactions have a maximum size of 100KB, and you have created a transaction over that size. The solution is to break up the transactions into chunks under 100KB each.
To do this:
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View -> "Show Coins." Click on the "Coins" tab.
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Select about 500 inputs in the Coins Tab
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Alt-click and select "Spend"
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Click Preview and check the size.
The transaction below is 212 KB - over the 100 KB limit. You can see that it has over 1500 inputs.

I'm going to select fewer inputs until the size is under 100KB - this one is 89KB with 633 inputs.

Now it will be successfully accepted by the Bitcoin network.
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