Nikah with a widow is not only a Sunnah but a social need also:

It is a social need because it is more complicated and risky for a woman who had enjoyed the pleasures of marriage and the company of a man to live without a man as compared to an unmarried woman.

If a widow is not married again then the possibility of her being corrupted is greater than an unmarried girl.

That is why in an Islamic society it is a command to marry with the widows. Even the widows are allowed to marry themselves so that they can choose a husband for themselves.

So much so that if the late husband has written a will that after his death his wife will be provided with the food and clothing and shelter for one year. i.e. seven months and twenty days more than the term (iddat) she will get for her social needs from her late husband's property, even then she is permitted to find a new companion and settle with him after her term (iddat). 
However, in this case, she will have to leave the food and clothing by her late husband's will.

“And those among you who die and leave the women behind (then they should
leave) a will for their women that they will be provided by their social
needs for one year without leaving the home. 
However, if they leave the home (of their late husband) themselves then you have no burden of it, which they have done for themselves in their own betterment.”

The above-mentioned verse shows that this kind of will is ordered to be
made according to the needs of the women in which the women enjoy the right to take the benefits of this will until one year. 
In this way, the Quran has made it the responsibility of the heirs of the late husband to meet the financial needs of the widow till at least one year and during this period woman is also free to find another, Kafil i.e. husband for the rest of her life In verse 4 Surah Al-Nisa,

Muslim men have been commanded to make widows their wives.

In verse 141 & 235 of Surah Al- Baqarah, the widows themselves have been made free for their own Nikah; and the verse 235 of Surah Al-baqrah motivates the men to marry widows. Now see the verse in which the collective conscience of the society has been addressed to take care of the marriage of all the unmarried people of the society.

“And marry such of you who are unmarried”.

Singles are of two kinds:-

1. Who are not married yet.
2. Married once but now lost the spouse.

Those who stop the widows to remarry should think about what they are doing because Quran has made it responsibility or even the whole Islamic society to find out a way for the unmarried people to marry and not to create obstacles in their way.

Sabeeaa binte Al- Haris Al- aslamya was pregnant at the time of her husband's death. The time for delivery was forty days with some difference in traditions. After delivery when she decided to marry then it was supposed to be inappropriate. Then she asked the matter from Hazrat Muhammad (saw) and he said: If you want to remarry then do it because your term (iddat) is completed with the delivery” (It means that there is no need to complete the term for four months and ten days). Although in this tradition there is a difference of opinion in the determination of the term (iddat), however even it also shows that one should make haste in remarrying.

The importance and virtue of marrying the widows can be seen from the fact that the first Nikah which our Holy Prophet made was with a widow and even after her death, the marriages he made were mostly with widows.

References:
1. Al-Nisa/3
2. Al-Baqarah/234
3. Al-Noor/32
4. Syed Muhammad Aloosi Baghdadi (d.1270H) Ruh-ul-Ma?ani fi tafseer ul Quran-ul-Azeem wa Al-Sab-ul-Masani, vol.28, p.138, Maktaba-e-Imdadia, Multan.