if you know you need to cbet most of the time, estimate the combinations of hands you check and see if the ratio makes sense, and do the inverse if you are checking most of the time and betting very little

so the most common hands checked here are weak Tx, 55-99, A4s A3s, basically weak pairs - how many combos is that compared to if you bet everything else? without doing the actual math it seems okay to me, you might not find the exact 25 check 75 bet but your close enough since your betting combos of overcards is going to outweigh your checked hands by quite a bit

Before you get too far into your analysis, how often are your C Bets in 3b pots successful in this dynamic? In general, its going to be somewhere between 35 to 40% depending on site/pool/stake. Won't fluctuate too much more up or down from that range.

So, if you are going to approach this from a high frequency approach, you are likely to fine mostly betting here. I would mostly bet this. We benefit from getting folds from something like 76s or some other combo drawing super live against your pair. I would be selective with my checks and consider checking Tx since it is less vulnerable against middling cards and could extract from their turn bluffs/thin value bets better than A4s which we likely end up folding on a ton of turns.

If you choose the more polar route, we can certainly bet big with TPTK+ but that is still a ton of combos. A4s probably still makes it in there to try to protect/get value when he has 65s and 76s.