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).