Large Numpy Scipy CSR Matrix, row wise operation

I want to iterate over the rows of a CSR Matrix and divide each element by the sum of the row, similar to this here:

numpy divide row by row sum

My problem is that I'm dealing with a large matrix: (96582, 350138)

And when applying the operation from the linked post, it bloats up my memory, since the returned matrix is dense.

So here is my first try:

for row in counts:
    row = row / row.sum()

Unfortunately this doesn't affect the matrix at all, so I came up with the second idea to create a new csr matrix and concat the rows using vstack:

from scipy import sparse
import time

start_time = curr_time = time.time()
mtx = sparse.csr_matrix((0, counts.shape[1]))
for i, row in enumerate(counts):
   prob_row = row / row.sum()
   mtx = sparse.vstack([mtx, prob_row])
   if i % 1000 == 0:
      delta_time = time.time() - curr_time
      total_time = time.time() - start_time
      curr_time = time.time()
      print('step: %i, total time: %i, delta_time: %i' % (i, total_time, delta_time))

This works well, but after some iterations it gets slower and slower:

step: 0, total time: 0, delta_time: 0
step: 1000, total time: 1, delta_time: 1
step: 2000, total time: 5, delta_time: 4
step: 3000, total time: 12, delta_time: 6
step: 4000, total time: 23, delta_time: 11
step: 5000, total time: 38, delta_time: 14
step: 6000, total time: 55, delta_time: 17
step: 7000, total time: 88, delta_time: 32
step: 8000, total time: 136, delta_time: 47
step: 9000, total time: 190, delta_time: 53
step: 10000, total time: 250, delta_time: 59
step: 11000, total time: 315, delta_time: 65
step: 12000, total time: 386, delta_time: 70
step: 13000, total time: 462, delta_time: 76
step: 14000, total time: 543, delta_time: 81
step: 15000, total time: 630, delta_time: 86
step: 16000, total time: 722, delta_time: 92
step: 17000, total time: 820, delta_time: 97

Any suggestions? Any idea why vstack gets slower and slower?