dip water, estimate
斟 centers on carefully measuring or gauging something, whether physically dipping water to assess its amount or figuratively estimating a situation.
斟 combines 甚 (likely contributing the sound) with 斗 (a measuring dipper), suggesting the act of measuring or dipping liquid. The exact historical development is uncertain.
The left side 甚 suggests something substantial, and the right side 斗 is a measuring dipper. Picture dipping a dipper into water to carefully estimate how much is there.
For シン, imagine a thin dipper (斗) being used to measure water: thin -> シン, and the dipper dips in to estimate the amount.
taking into consideration; making allowances (for)