First: the idea of 'weak blocks' (hat tip to Rusty for the term) is for miners to pre-announce blocks that they're working on, before they've solved the proof-of-work puzzle. To prevent DoS attacks, assume that some amount of proof-of-work is done (hence the term 'weak block') to rate-limit how many 'weak block' messages are relayed across the network.
Today, miners are incentivized to start mining an empty block as soon as they see a block with valid proof-of-work, because they want to spend as little time as possible mining a not-best chain.
Imagine miners always pre-announce the blocks they're working on to their peers, and peers validate those 'weak blocks' as quickly as they are able.
Because weak blocks are pre-validated, when a full-difficulty block based on a previously announced weak block is found, block propagation should be insanely fast-- basically, as fast as a single packet can be relayed across the network the whole network could be mining on the new block.
I don't see any barrier to making accepting the full-difficulty block and CreateNewBlock() insanely fast, and if those operations take just a microsecond or three, miners will have an incentive to create blocks with fee-paying transactions that weren't in the last block, rather than mining empty blocks.
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A miner could try to avoid validation work by just taking a weak block announced by somebody else, replacing the coinbase and re-computing the merkle root, and then mining. They will be at a slight disadvantage to fully validating miners, though, because they WOULD have to mine empty blocks between the time a full block is found and a fully-validating miner announced their next weak block.
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Weak block announcements are great for the network; they give transaction creators a pretty good idea of whether or not their transactions are likely to be confirmed in the next block. And if we're smart about implementing them, they shouldn't increase bandwidth or CPU usage significantly, because all the weak blocks at a given point in time are likely to contain the same transactions.