The rulebook states that carrying capacity is the strength score times 15 (lbs). Find familiar allows me to get a hawk, which has a strength score of 5. This results in a carrying capacity of 75 lbs. This is well within the range of weights for small people such as gnomes or halflings. Does this mean my familiar can carry them and fly away (given they do not struggle)?
Yes, a familiar can carry loads if it can properly grip or support them, including a willing creature if they fall within this weight limit. However, a hawk can only carry 37.5 pounds, as it is a Tiny creature, and thus its carry capacity is halved (PHB 176 'Size and Strength').
Yes, well sort of yes.
- Take at least two levels in Druid.
- Gain access to the Find Familiar spell (Magic initiate feat if you don't want to be a wizard). Use it to find a hawk familiar.
- Wild Shape yourself into a creature lighter than 18.75 lbs.
- Success! (sort of)
With a kobald and a hawk familiar(can carry 37.5lbs) it will work kobalds weighing 30lbs alone, you could carry an extra 7.5lbs of equipment while flying.