Maximum thrust-to-weight is usually less than 100% on most aircraft... a few fighters are exceptions in that they can actually hover and climb straight up. Most planes are unable to hover and fly and take off by lift.
Typical thrust/weight ratios of transport airplanes at MTOW seem to be in the range of 25 %...35%. Lift is of course over 100 %.
Most transport planes are actually unable to reach the maximum (stalling) lift coefficient on ground, because they would then have a tailstrike. The maximum lift coefficient is thus limited by the tail clearance needed for safety.
I think that when the MTOW is limited by air density (hot and/or high conditions), the certification requirement is for a certain climb slope to be achieved with one engine inoperative. This slope is something like 2,4 % for 1 out of 2 engines, 2,7 % for 2 out of 3 engines, 3,0 % for 3 out of 4 engines. So presumably the thrust/weight ratio has to be the slope required + the drag.