The speech of Allāh is heavy in multiple ways, He ﷻ says,
"𝑾𝒆 𝒘𝒊𝒍𝒍 𝒔𝒆𝒏𝒅 𝒅𝒐𝒘𝒏 𝒖𝒑𝒐𝒏 𝒚𝒐𝒖 𝒂 𝒘𝒆𝒊𝒈𝒉𝒕𝒚 𝒔𝒑𝒆𝒆𝒄𝒉" [73:5]

Heavy in its
- Revelation
- Recitation
- Learning/memorising
-Teaching
- Status
- Reward

[THREAD]

𝗙𝗶𝗿𝘀𝘁𝗹𝘆, the Qur'ān is heavy in its revelation
Nabī ﷺ would experience alot of difficulty when receiving revelation  to such an extent even on a cold day Nabī ﷺ would perspire.

Likewise, if revelation was descending whilst he ﷺ was sat on a camel, the camel would be compelled to sit due it not being able to bear the weight of the Qur'ān.

Secondly, in it's recitation
To aspire to read the Qur'an correctly, abiding by the laws of Tajwīd, ensuring all Makhārij are being pronounced correctly and reciting with the correct pace is not easy. It requires effort to learn, effort to master and effort to pass on to others.

𝗧𝗵𝗶𝗿𝗱𝗹𝘆, in its learning
To dedicate time on a daily bases to memorise/learn the Qur'an is something that requires sacrifice, giving up ones desires and dedicating oneself to the Kalām of Allāh. To memorise/learn the Qur'an is challenging, even burdensome at times.

𝗙𝗼𝘂𝗿𝘁𝗵𝗹𝘆, the Qur'ān is heavy in its teaching
Passing the Qur'ān onto others correctly is taxing, more so since its learning is so challenging.

After the third and fourth point it becomes clearer as to why Nabī ﷺ said,
"𝘛𝘩𝘦 𝘣𝘦𝘴𝘵 o𝘧 𝘺𝘰𝘶 𝘢𝘳𝘦 𝘵𝘩𝘰𝘴𝘦 𝘸𝘩𝘰 𝘭𝘦𝘢𝘳𝘯 𝘵𝘩𝘦 𝘘𝘶𝘳'ā𝘯 𝘢𝘯𝘥/𝘰𝘳 𝘵𝘦𝘢𝘤𝘩 𝘪𝘵."

𝗙𝗶𝗳𝘁𝗵𝗹𝘆, it holds a heavy status
Allāh will elevate the status of the one who learns the Qur'ān, masters its sciences and passes it on in this world and in the Afterlife

𝗙𝗶𝗻𝗮𝗹𝗹𝘆, it is weighty in reward - ثقيلا اجره
The reward of the Qur'an is very great and magnificent.

(main points taken from the explanation of Mufti Radhā-ul Haqq for this Āyah)