Every depth block will cost computation power, am I right?
If the amount of transaction is very small, and the depth is infinite, will it become a burden to whole bitcoin system?
yes, it is the "work" miners do in bitcoin because of its "proof of work" algorithm to find a new block. that work takes computation power which increases/decreases based on difficulty which then adjusts based on how many miners (ore more accurately how much hashrate) is going into mining bitcoin.
it is not a burden, it is how bitcoin works. the chain will continue growing just like it has been growing for the past 11 years (ie. the entire lifetime of bitcoin).
keep in mind that the transaction and its block are verified
only once when the node receives them.