(And those who dispute concerning Allah, after it has been accepted,) means, those who dispute with the believers who have responded to Allah and His Messenger, and try to stop them from following the path of guidance.
حُجَّتُهُمْ دَاحِضَةٌ عِندَ رَبِّهِمْ
(no use is their dispute before their Lord) means, it is futile before Allah.
وَعَلَيْهِمْ غَضَبٌ
(and on them is wrath,) means, from Him.
وَلَهُمْ عَذَابٌ شَدِيدٌ
(and for them will be a severe torment.) means, on the Day of Resurrection. Ibn `Abbas, may Allah be pleased with him, and Mujahid said, "They disputed with the believers after they responded to Allah and His Messenger, and tried to prevent them from following the path of guidance, hoping that they would return to Jahiliyyah." Qatadah said, "These were the Jews and Christians who said to them, `Our religion is better than your religion, our Prophet came before your Prophet, and we are better than you and closer to Allah than you. "' This was nothing but lies. Then Allah says:
This fact is stated in the next sentence, أَنزَلَ الْكِتَابَ بِالْحَقِّ وَالْمِيزَانَ "has sent down the Book with truth and the Balance as well - 17." Here ` the Book' means the Qur'an, and all the previous revealed Books, and ` truth' means the divine religion mentioned above, and ` the Balance' literally means a weighing balance. Since it is an instrument of weighing one's due and establishing justice, Sayyidna Ibn ` Abbas ؓ has taken it to mean ` equity' and ` justice'. Mujahid (رح) leading exegete, has said that here the ` Balance' means full payment of everyone's rights and doing justice. As such the word ` truth' points towards Allah's rights over His servants, and the word مِیزَان mizan (Balance) points towards the rights of human beings over one another.
The statement that those who believe are fearful of the Doomsday means the fear generated due to cognizance of the awesome horrifying happenings which will take place on the Doomsday, and also due to cognizance of one's own short comings and wrong-doings. However, sometimes a believer's eagerness to meet his Lord Allah Almighty overcomes that fear, which does not contradict this statement; some dead ones are proved to have said in their graves that they wish Doomsday would come soon because the glad tidings given by angels that they would be forgiven and treated kindly, had overcome the fear of Doomsday.
Tazkirul Quran
Maulana Wahiduddin KhanOn ayahs 16–17
Here the ‘Book’ means the original religion which was revealed through the prophets and ‘desire’ (ahwa’) refers to the fabrications which human beings on their own added to the original religion of Truth. The Prophet was instructed to be firm on the original religion. Even on the grounds of dawah considerations, he was forbidden to make any concessions to man-made religions. He was told that his duty was to uphold justice, i.e. to take decisions about religious differences and show what was right and what was wrong; which part was from God and which was later added to religion by way of human interpolation. ‘There is no contention between us and you’ means that, in spite of your quarrelling with us, we will not start quarrelling with you. In other words, even if you introduce negative tactics, we will unilaterally adhere to our positive approach. The responsibility of a dayee is simply to convey the message of Truth. All other matters are left to God. Harassing those who have accepted the Truth and embroiling them in unnecessary wrangling is the most oppressive and unworthy practice. Those who do so run the risk of incurring the wrath of God and facing severe punishment in the Hereafter.
Uthmani text of the Madinah mushaf (King Fahd Complex). Translation: Saheeh International. Tafsir via Quran.com.