Preflop defend is standard, flop check is preferred with 8h7h; once we raise and get called, the Jh turn is a strong card for our range, so we should continue barreling for real, not with a tiny stab.
9h4h2c is a semi-wet, draw-heavy board where BU has a slight range advantage. With 8h7h we have a strong flush draw and decent equity, but theory leans heavily toward checking this combo rather than leading a big raise. If we do choose to lead, a small sizing is preferred; the large raise mostly gets action from stronger made hands and higher flush draws.
The Jh is a very good card for our range: we now have the nut flush draw and a strong semi-bluff candidate. After we flop-raise and get called, we should continue barreling for real on this turn, targeting BU's one-pair and weaker heart holdings. A tiny 0.6BB bet barely pressures those hands and doesn't meaningfully increase fold equity; a larger sizing (around 60–70% pot) is preferred to extract value and fold out weaker holdings.