Are you at risk of a heart attack? If so it is probably useful. Seriously, I have a (mid-fifties) friend whose doctor advised him that everybody "over a certain age" should wear a HRM when they exercise.
Also, there is a regime of training that is heart-rate-based. Clearly if you subscribe to this, then you will need a heart rate monitor to see how you're doing. But there are also regimes which emphasise cadence, or power, or probably other parameters too. So heart rate is not the only metric by which to judge "progress".
But since you say you're cycling for weight loss, would it be fair to say that none of these specific metrics interests you (yet)? In which case, I wouldn't get too stressed about not having a HRM. If what you want is weight loss, getting on the bike in the first place will start to achieve that.
One thing I would say - and I am someone who started cycling to achieve weight loss, and who has worn a HRM since the start - is that by measuring things like heart rate data over time, you get to know how your body is working, what its limitations are, how your fitness is improving etc., which can be useful. But is it useful enough to go buy an HRM? Well, that's really your call. (After all, if all you're interested in is weight loss, then a set of scales will suffice!)
Lastly I'd echo what @Batman says - if you think there's any cardio risk with you jumping on a bike in the first place, you should really consult your doctor before doing so.