DataFrame memory_usage inflates when unpickling a MultiIndex, deflates after copy
#### Code Sample, a copy-pastable example if possible

```python
import numpy as np
import pandas as pd
size = 1000*1000
idx = pd.Series([0,1,2,3]).sample(size, replace=True)
df = pd.DataFrame({'idx': idx, 'prog': np.arange(size)}).set_index(['idx', 'prog'])
# df = pd.DataFrame({'idx': idx, 'prog': np.arange(size)}).set_index('idx')
df.to_pickle('DELETEME.pkl')

df.memory_usage(deep=True, index=True) # small
loaded_df = pd.read_pickle('DELETEME.pkl')
loaded_df.memory_usage(deep=True, index=True)/2**20 # big
loaded_df.copy().memory_usage(deep=True, index=True)/2**20 # small again

```
#### Problem description

When a dataframe with a multiindex is pickled and then reloaded, its "memory_usage" increases by many times (in the example, approximately x4). If the dataframe is copied after reading, the memory_usage goes back to its original value. This does not happen with columns or with simple indices (non-multiple ones).

#### Current Fix
When I read pickles which I know have a MultiIndex, I copy right after reading.

#### Expected Output

The size of a dataframe should not change much when pickling and unpickling, or if there is a reason why it should do so specifically when working with a MultiIndex, this could be mentioned in the documentation.

#### Output of ``pd.show_versions()``

<details>

commit           : None
python           : 3.7.5.final.0
python-bits      : 64
OS               : Darwin
OS-release       : 18.6.0
machine          : x86_64
processor        : i386
byteorder        : little
LC_ALL           : en_US.UTF-8
LANG             : en_US.UTF-8
LOCALE           : en_US.UTF-8

pandas           : 0.25.2
numpy            : 1.17.3
pytz             : 2019.3
dateutil         : 2.8.1
pip              : 19.3.1
setuptools       : 41.6.0.post20191030
Cython           : None
pytest           : None
hypothesis       : None
sphinx           : None
blosc            : None
feather          : None
xlsxwriter       : None
lxml.etree       : None
html5lib         : None
pymysql          : None
psycopg2         : None
jinja2           : None
IPython          : None
pandas_datareader: None
bs4              : None
bottleneck       : None
fastparquet      : None
gcsfs            : None
lxml.etree       : None
matplotlib       : None
numexpr          : None
odfpy            : None
openpyxl         : None
pandas_gbq       : None
pyarrow          : None
pytables         : None
s3fs             : None
scipy            : None
sqlalchemy       : None
tables           : None
xarray           : None
xlrd             : None
xlwt             : None
xlsxwriter       : None
</details>
