Closing costs vary some from bank to bank or lending institution, but have very little to do with the price of the house.
Closing costs are generally around $2000 moe or less.
They include fees such as title search, document fees, appraisal, and service fees.
While a few banks do things 'in house", most use an Abstract firm. The firm will charge a fee for the use of their facility, their time and leg work neccesary to make sure all the paperwork is legal and "in order" before you "sign" (many times you will sign your name).
The closing costs should be the same for a $100,000 as a $400,000 home. Sometimes they have to be paid up-front, while other times they can "roll it in" to the loan.
P..S. Occasionally, you can negotiate "some" of the costs. As I did last time I re-financed. The abstract company was going to charge $700 just for the use of their building, so instead we did everything "in house" on the loan officer's desk That brought my closing costs down from $2100 to about $1400. Sometimes you just have to "work" on people.