BUG: Setting the index changes dtype
- [x] I have checked that this issue has not already been reported.

- [x] I have confirmed this bug exists on the latest version of pandas.

- [ ] (optional) I have confirmed this bug exists on the master branch of pandas.

---

**Note**: Please read [this guide](https://matthewrocklin.com/blog/work/2018/02/28/minimal-bug-reports) detailing how to provide the necessary information for us to reproduce your bug.

#### Code Sample, a copy-pastable example

```python
import pandas as pd
import numpy as np

df = pd.DataFrame({'A': [1,2,3], 'B': [1,10,100]}).astype(np.uint16)
print(df.dtypes)
# A    uint16
# B    uint16
# dtype: object

df = df \
  .set_index('B') \
  .reset_index()
print(df.dtypes)
# B    uint64
# A    uint16
# dtype: object

```

#### Problem description

In the example above the type of column `B` changed from `uint16` to `uint64`. It may cause the memory issue, so expected behavior is to not change the types implicitly.

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

<details>

INSTALLED VERSIONS
------------------
commit           : None
python           : 3.6.9.final.0
python-bits      : 64
OS               : Linux
OS-release       : 4.19.104+
machine          : x86_64
processor        : x86_64
byteorder        : little
LC_ALL           : None
LANG             : en_US.UTF-8
LOCALE           : en_US.UTF-8

pandas           : 1.0.3
numpy            : 1.18.4
pytz             : 2018.9
dateutil         : 2.8.1
pip              : 19.3.1
setuptools       : 46.3.0
Cython           : 0.29.18
pytest           : 3.6.4
hypothesis       : None
sphinx           : 1.8.5
blosc            : None
feather          : 0.4.1
xlsxwriter       : None
lxml.etree       : 4.2.6
html5lib         : 1.0.1
pymysql          : None
psycopg2         : 2.7.6.1 (dt dec pq3 ext lo64)
jinja2           : 2.11.2
IPython          : 5.5.0
pandas_datareader: 0.8.1
bs4              : 4.6.3
bottleneck       : 1.3.2
fastparquet      : None
gcsfs            : None
lxml.etree       : 4.2.6
matplotlib       : 3.2.1
numexpr          : 2.7.1
odfpy            : None
openpyxl         : 2.5.9
pandas_gbq       : 0.11.0
pyarrow          : 0.14.1
pytables         : None
pytest           : 3.6.4
pyxlsb           : None
s3fs             : 0.4.2
scipy            : 1.4.1
sqlalchemy       : 1.3.17
tables           : 3.4.4
tabulate         : 0.8.7
xarray           : 0.15.1
xlrd             : 1.1.0
xlwt             : 1.3.0
xlsxwriter       : None
numba            : 0.48.0

</details>
