How Bitcoin will scale into the future is a topic of much debate. I will try to steer clear of too much opinion, and just give you the basic factors at play.
First, understand that there are different types of nodes on the Bitcoin network. There are nodes that mine, there are nodes that keep full copies of the blockchain, and there are thin client nodes that only store the information required to maintain a single wallet.
The thin clients are what make up the vast majority of network participants, since this is what a normal user of the Bitcoin network will be running. Since they don't store the blockchain, they don't care how much it grows. The other two types of nodes are the ones where we are concerned with centralization. They are what really represent the infrastructure of the system.
First, there are "full nodes", which keep full copies of the blockchain on hand. These nodes provide requesting clients with historical blocks and transactions stored in their databases. They also relay current transactions and blocks to other nodes, and verify the validity before passing the data on to other peers. This provides the "plumbing" of the network and a first line of defense against malicious network participants. It should be stated that there is no direct financial incentive for running a full node, yet it does require you to store the full blockchain (although some pruning is okay).
Second, there are mining nodes. As the network has evolved from the specs laid out in the original whitepaper, mining nodes have become hyper-specialized. Where at first, all full nodes had the option of mining, nowadays nearly all mining is done by mining pools. These pools run their own networks of participants, and those participants only deal with hashing blocks they receive from the hub of the mining pool. The nodes actually doing the mining are not running full nodes, but are relying on the mining hub to run full nodes and participate in the Bitcoin network. Although the miners, themselves, can be very decentralized, there is already a certain degree of centralization of mining pool operators. However, this is not due to the size of the blockchain, which is a negligible cost to a mining pool.
So, as the blockchain grows, it makes it less and less feasible to run a full node, yet this is not a problem for mining nodes and pools. Full nodes are not paid for their service, so it becomes harder to justify running one if the data storage becomes expensive. Luckily, data storage costs trend downward at a geometric pace, while the blockchain grows linearly (currently ~1MB/10min). This means it is still feasible to run a full node for the foreseeable future.
I should also note that although there isn't a direct financial incentive for running a full node, there are several indirect incentives. Running a full node allows a network participant to operate in a trustless manner. This is important to many people for a variety of reasons. For example, any online wallet or exchange company would typically need to run their own full nodes so that they don't have to rely on others for their core business. There are many other reasons to run a full node as well, which will help to counteract centralization.