Is lightning network limited by the 'size' of channels?
In fact, it's worse: payment channels can only transfer the balance that belongs to the sender in it. So, if David and Rob each paid 25BTC into the channel, David can at most send 25 BTC to Rob.— However, there could actually be multiple paths from Alice to Rob which could in parallel allocate 100BTC to Rob.

There's an interesting trade-off here: the Bitcoin blockchain scales easily in the amounts to be settled, but is limited in transaction throughput. Lightning Network on the other hand is practically unlimited in the transaction throughput, however limited in the amounts to be sent. This is why transactions on the blockchain are priced by the cost of including them in the block, i.e. the primary bottleneck, and transactions in the Lightning Network will probably be priced mostly relative to the value they transfer. Obviously, this favors larger value transfers on the blockchain and smaller payments to move to the Lightning Network. However, sending smaller payments requires both a smaller locked-in amount, and will make it easier to find routes.

So, it may actually just work out.— We'll see when it goes live on the Bitcoin blockchain.