// Use the mysql week() or weekofyear() functions.
No, you cannot retrieve all week numbers between dates in one query without a stored function or procedure. What you would need is a function which returns a result set of more than one row with two input parameters for the limiting dates. I do not think it is possible.
But you could create a table with 366 values (one for each day) and then link it into a join query which selects all the day numbers between two given day numbers. From this result you might build a query which returns the week numbers for the dates in between.
by smantscheff: Other answers came while I was editing.