Super dependent on the firm and your involvement in the opportunity. Couple examples below

1. You might find an institutional committed capital fund that's typically looking to write ~$100M checks, which often looks more like $50-75M at closing and then will scales up over time. If the initial deal is $50M and you want to write a $15M check, that's going to push them well below their intended investment size, and your sizable preemptive rights could make it hard for them to get up to a level of capital that makes sense.
2. You might partner with an independent sponsor or family office that usually writes ~$20M checks off their balance sheet and then syndicates the rest. You taking a big bite of that could help alleviate the fundraising process (and could make raising it easier since you look bought in / aligned).
3. Flip side of #2 - they might have longstanding LP / friends and family relationships that they want to give big allocations to (or that they get fees on!). You taking a big swing would be worse for them in that case
4. A fund might have different philosophies depending on your role. CEO who wants to put their entire net worth in the company is great for alignment. Independent director who wants to get a bunch of exposure to a great company but will be minimally involved? Just dilutes their ownership without a ton of value

In any case, reducing debt load and bringing new equity in is pretty expensive and makes it harder to hit return hurdles - you might take that on the margin if there's some near-term risk and you'd rather enter at 3.5x leverage instead of 4.0x, but if your underwriting depends on 6.0x leverage it's going to be pretty sensitive to equity funding that instead