Is there a PoW system that shows cumulative work without an ever-increasing proof size? Let's say I have an output in the blockchain at height 100,000. At height 200,000, I want to prove that my output has the work of 100k blocks built onto it, securing it. In Bitcoin, proving that the output has X number of hashes securing it requires providing the full chain of headers, or 80 bytes * 100,000. 

Is there an alternative proof of work where these 'work-proofs' do not grow in size indefinitely?

EDIT:

Now that I have found some resources, the terminology for I was looking for is "compact SPV proofs".
There's a suggested change to Bitcoin (adding skiplists to the header) that would make that quite possible. See Appendix B of Blockstream's sidechains paper,  Efficient SPV Proofs:


  The inspiration for compact SPV proofs is the skiplist [Pug90], a probabilistic
  data structure which provides log-complexity search without requiring rebalancing (which is good
  because an append-only structure such as a blockchain cannot be rebalanced).
  We require a change to Bitcoin so that rather than each blockheader committing only to the
  header before it, it commits to every one of its ancestors. These commitments can be stored
   in a Merkle tree for space efficiency: by including only a root hash in each block, we obtain a
  commitment to every element in the tree. Second, when extracting SPV proofs, provers are allowed
  to use these commitments to jump back to a block more than one link back in the chain, provided the
  work actually proven by the header exceeds the total target work proven by only following direct
  predecessor links. The result is a short DMMS which proves just as much work as the original
  blockchain.
  
  [...]
  
  Therefore if we want to skip the entire remaining chain in one jump, we expect to search only
  halfway; by the same argument we expect to skip this half after only a quarter, this quarter after
  only an eighth, and so on. The result is that the expected total proof length is logarithmic in the
  original length of the chain.
  For a million-block chain, the expected proof size for the entire chain is only log2(1000000) ≈ 20
  headers. This brings the DMMS size down into the tens-of-kilobytes range.


Also see Mark Friedenbach's Email on the bitcoin-dev mailing list concerning compact SPV proofs: http://sourceforge.net/p/bitcoin/mailman/message/32111357/