Grading: This hadith is sahih, and this chain is "hasan" on account of Yahya bin Ayyub (Abu al-'Abbas al-Ghafiqi al-Misri).

Reference / Source: Abu al-'Abbas al-Asamm narrated it in "Majmu' fihi Musannafatuh" (303), al-Tabarani in "al-Awsat" (3145), and Ibn Jumay' al-Saydawi in "Mu'jam Shuyukhih" (76), through the chain of Shu'ayb bin Yahya al-Tujibi from Yahya bin Ayyub al-Ghafiqi.
Technical note / Defect ('illah): Imam al-Tabarani says that no one narrated it from Humayd except Yahya (bin Ayyub).

Corroborating chains and supporting reports: Yahya bin Ayyub was corroborated in this wording by Khalid bin 'Abdullah al-Wasiti (Abu Dawud: 4863) and by 'Abd al-Wahhab al-Thaqafi (al-Tirmidhi: within hadith 1754).

Note / Clarification: It should be pointed out here that the old manuscripts of al-Tirmidhi have the word "yatawakka'u" (walking while leaning), and Imam al-Baghawi narrated it thus from Imam al-Tirmidhi in "Sharh al-Sunnah" (3640), and al-Diya' al-Maqdisi also said the same about al-Tirmidhi's narration in "al-Mukhtarah" 5/ (1949). However, some later manuscripts of al-Tirmidhi have the word "yatakaffa'u" (walking inclined forward, or briskly), and 'Allamah al-Mubarakpuri commented on that in "Tuhfat al-Ahwadhi".

Reference / Source: Ibn 'Asakir narrated it in "Tarikh Dimashq" 3/ 278 by way of 'Ali bin 'Asim; al-Ajurri in "al-Shari'ah" (1019) and al-Silafi in "al-Mashyakhah al-Baghdadiyyah" (24) by way of Mu'tamir bin Sulayman; and al-Bayhaqi in "al-Dala'il" 1/ 274 and "al-Adab" (665), and Ibn 'Asakir in 3/ 279, by way of Ibrahim bin Tahman; all three ('Ali, Mu'tamir, Ibrahim) narrate it from Humayd.
Technical note / Defect ('illah): There is inconsistency (idtirab) in these narrations, to the extent that within one and the same chain the word is sometimes reported as "yatakaffa'u" and sometimes as "yatawakka'u".

Reference / Source: Imam Ahmad 21/ (13381, 13851), Imam Muslim (2330) (82) and Ibn Hibban (6310) narrated it by way of Hammad bin Salamah from Thabit from Anas (may Allah be pleased with him), with the word "takaffa'a".

Important point: The word "yatawakka'u" means to lean on a staff or the like, and its form is that the walker leans forward as he walks. Some scholars, such as Ibn al-Athir, took "al-takaffu'" in this same meaning, whereas the well-known description of the gait of the Prophet (peace and blessings be upon him) is that he (peace and blessings be upon him) walked with strength and speed. That is why 'Ali (may Allah be pleased with him), describing him (peace and blessings be upon him) (in the previous hadith 4239), said: "When he (peace and blessings be upon him) walked, he leaned forward (walking briskly) as though he were descending a slope." In the hadith of Laqit bin Sabirah (530) it says: "The Messenger of Allah (peace and blessings be upon him) came, lifting his feet firmly from the ground and leaning forward." Its meaning is that when he (peace and blessings be upon him) walked, he lifted his feet from the ground with force.

Reference / Source: In the hadith of Ibn 'Abbas (may Allah be pleased with them) (Musnad Ahmad: 5/ 3033) it says: "When he (peace and blessings be upon him) walked, he walked with his whole body gathered together, with no sluggishness in it."
Note / Clarification: Caution: In the manuscripts, after this hadith, the same hadith was recorded again from Ibn Abi Maryam to its end, so we have deleted the repeated portion.