Mahasi Sayadaw Walking In the tradition of Ven. Mahasi Sayadaw, it is taught that walking and sitting meditation should be practiced balanced with one another. I am wondering where it can be found that the Buddha taught this, or how the venerable sir came to this instruction. Thank you.
The Buddha did in fact teach just this practice:

Bhikkhus, you should train thus: ‘We will be devoted to wakefulness. During the day, while walking back and forth and sitting, we will purify our minds of obstructive states. In the first watch of the night, while walking back and forth and sitting, we will purify our minds of obstructive states. In the middle watch of the night we will lie down on the right side in the lion’s pose with one foot overlapping the other, mindful and fully aware, after noting in our minds the time for rising. After rising, in the third watch of the night, while walking back and forth and sitting, we will purify our minds of obstructive states.’
-- MN 39 (Bodhi, trans)

This passage occurs frequently in the suttas. The Buddha taught there are five benefits to walking meditation:

addhānakkhamo hoti - one is able to tolerate long-distance travel
padhānakkhamo hoti - one is able to tolerate exertion
appābādho hoti - one has little sickness
asitaṃ pītaṃ khāyitaṃ sāyitaṃ sammā pariṇāmaṃ gacchati - what is eaten, drunk, chewed and tasted goes to proper digestion
caṅkamādhigato samādhi ciraṭṭhitiko hoti - walking-produced concentration is of long duration.

-- AN 5.29